4. Find the areas contained in the shapes. 7. Find the areas contained in the shapes.

Size: px
Start display at page:

Download "4. Find the areas contained in the shapes. 7. Find the areas contained in the shapes."

Transcription

1

2

3

4

5 Geometry Name: Composite Area I Worksheet Period: Date: 4. Find the areas contained in the shapes. 7. Find the areas contained in the shapes. 4 mm 2 mm 2 mm 4 cm 3 cm 6 cm 4 cm 7 cm 9. Find the shaded area. 11. Delta's backyard is rectangular. Its dimensions are 15.0 m by 10.0 m. Delta's family is making a garden from the patio doors to the corners at the back of the yard. The patio doors are 2.0 m wide. Determine the area of the garden. Show your work. Worksheet Composite Areas II 7. Find the area contained in an isosceles right triangle with semi circles attached to each side. 9. Calculate the non shaded area: 8 cm 8 cm cm

6 10. Calculate the non shaded area: 13. Calculate the shaded area: in Find the value of h. (Hint: Find the area using 10 as the base; then use that area to work backwards to find the h with 8 as the base.) 8 h Sonja wants to place a decorative brick edging around a flower garden that is in the shape of a rhombus. One diagonal is 30 feet long, and the 15 area is 600 square feet. How many bricks must she purchase if each brick is one foot long? 19. Graph the lines and find the area of the triangle enclosed by the lines. y = 7 x = -3 y = 2x Find the area of quadrilateral QRST with vertices Q(-2, -1), R(-2, 2), S(2, 3), and T(1, -1). 15. Calculate the shaded area: 2 ft 12 ft 8 ft 4 ft 27 ft

7 10-3 and 10-5: Answers to Pg 548 # 2-26 (every 4th question), all, 32-33; Pg 561 # 2-26 (every 4th question), 20, 23, 33, 36. Pg 548 Pg m 4=90, m 5=45, m 6= in ,080 in = ft = ft m cm km in (a) 50 mm 2 ; (b) 116 mm (a) 30. (b) P = 45.3 in; A = 128 in m 1=36, m 2=18, m 3= P = 6.2 mi; A = 3 mi in ,459,000 ft m P = 17.6 ft; A = 21.4 ft m ft cm cm ft m m : Answers to Pg 569 # 8, (multiples of 5, omit #40), 51, 59-66, π in π ft (a) 0.5. (b) 2.5. (c) in. 60. (a) 25,000 mi. (b). The estimate seems quite accurate ft 60. a) 25,000 mi. b) Eratosthenes s estimate seems quite accurate. 61. (2.5, 5) 62. 5π units π ft π in 65. 3π m cm 70. (a) arcs BD and FE, or arcs AB and GF, or etc. (b) x= π in yd, yd, yd, yd, yd, yd, yd, yd. 10-4: Answers to Pg 555 # 2-8 evens, 9, evens, 25, :3, 16:9 4. 3:5, 9: m m 2 9. $ $ :2, 5: :4, 3: :10, 1: :5, 4: :4, 49: C cm x = 2 cm, y = 3 cm 28. x = 4 cm, y = 6 cm 30. x = 4 2 cm, y = 6 2 cm in by 12 in, 3 in by 16 in m a) 6 3 cm 2. b) 54 3 cm 2, cm 2, 96 3 cm always 42. sometimes 43. never 44. sometimes 10-7: Answers to Pg 577 # 2-26 evens, all, all, π cm 2 4. π / 9 in 2 6. about 22 ft π cm π in π cm π ft π cm ft m (243π +162) ft (120π ) m (64 16π) ft A 29. Lower outside has larger base area (8.75π in 2 ) than Top and Lower inside (8π in 2 ) circles in in. 35. (49π ) m (200 50π) m π m Blue region; let AB = 2x. Area of blue = 4x 2 πx 2. Area of yellow = πx 2 2x (c) 239 ft Answers to Pg 584 # 4, 6, 7, 10, 16, 18, all, all, even. 4. 2/5 or 40% 6. 3/10 or 30% 7. 2/5 or 40% 10. 4/7 or about 57% % 18. 2/3 or about 67% 20. (4 π)/4 or about 21% 21. 4% π/4 24. π/4 25. π/ π/200 or about 16% 27. a) 14 prizes. b) $ /5 or 60% 32. 3/ / /20 or 45% 38. 3/ about 46% 42. about 58% 44. a) yes. b) no. c) 2/3

8 Review: Similarity and Right Triangles G.11A, G.11B, G.8C, G.5D, G.11C Name: Date: Period: Similarity: TEKS: G.11A The student will use and extend similarity properties and transformations to explore and justify conjectures about geometric figures. TEKS: G.11B The student will use ratios to solve problems involving similar figures. 1. A triangle has side lengths 1, 1.5, and 2 units. Which of the following could be the lengths of the sides of a triangle that was formed by dilating the given triangle? A. 1, 3, and 4 units B. 2, 4, and 6 units 2. Ramon places a mirror on the ground 45 ft from the base of a geyser. He walks backward until he can see the top of the geyser in the middle of the mirror. At that point, Ramon s eyes are 6 ft above the ground and he is 7.5 ft from the mirror. Use similar triangles to find the height of the geyser. C. 4, 4.5 and 5 units x ft D. 4, 6, and 8 units 6 ft 45 ft 7.5 ft x Pythagorean Theorem: TEKS: G.8C The student will derive, extend, and use the Pythagorean theorem. 5. Find the area and perimeter of the following 6. Look at the drawing shown below. If Δ KMP is trapezoid. a right triangle formed by the placement of 3 squares, what is the area of the shaded square? 7. A parallelogram has sides measuring 8.5 cm and 12 cm and a diagonal measuring 15 cm. Is the parallelogram a rectangle? If not, is the 15 cm diagonal the longer or shorter diagonal?

9 8. Oscar's dog house is shaped like a tent. The slanted sides are both 5 feet long and the bottom of the house is 6 feet across. What is the height of his dog house, in feet, at its tallest point? 9. What type of triangle is formed by these side lengths: 8, 15, 17 50, 120, , 1.73, , 12, 18 Special Right Triangles: TEKS: G.5D The student will identify and apply patterns from right triangles to solve meaningful problems, including special right triangles ( and ) and triangles whose sides are Pythagorean triples. 10. Find the length of the diagonal of a square with perimeter x 11. Charles is looking out a window from a point 50 feet above the ground. When Charles looks down at an angle of depression of 30, he sees his dog Max. To the nearest foot, how far is Max from the base of the building? Charles 50 feet y x Max Trigonometry: TEKS: G.11C The student will develop, apply, and justify triangle similarity relationships, such as right triangle ratios, trigonometric ratios, and Pythagorean triples using a variety of methods. 13. Mr. Ryan flies in his airplane at an altitude of 2400 ft. He sees a cornfield at an angle of depression of 30. What is his approximate horizontal distance from the cornfield at this point? Airplane A man who is 6 feet tall is flying a kite. The kite string is 75 feet long. If the angle that the kite string makes with the line horizontal to the ground is 35, how far above the ground is the kite? 2400 ft Cornfield 15. A 12-foot ladder is leaning against a wall. If it is 4 feet from the base of the wall, what is the angle the ladder makes with the ground? 16. A tree has a shadow that is 31 feet long. If the angle created by the end of the shadow and the sun is 62, how tall is the tree?

10 Name: Date: Period: 17. What is the approximate length of FJ? 5 inches G F 18. Melissa is looking at a tall tree in her backyard at a 68 angle. She is standing 20 feet from the base of the tree. How tall is the tree? 8 inches H 8 inches J 19. (a) Determine whether the two triangles are similar. (b) If they are similar, state the theorem or postulate used to justify similarity. (c) Write the similarity statement. (d) Solve for x. 20. A kite string is 220 feet long from the kite to the ground. The string makes a 45 angle with the ground. About how high off the ground is the kite? LMN ~ by 21. Solve for x and y. 22. Find the amount of fencing needed for a rectangular yard with a diagonal of 39 m and one 12 side of 36 m. x y The diagram shows a portion of a bridge support. What is the distance from point B to point C? 24. A sailor in a boat is looking at the top of a 150- foot tall lighthouse that is 280 feet away. What is the angle of depression from the top of the lighthouse down to the sailor? C 120 ft B 40 ft 100 ft A E D

11 25. Mr. Schultz has a garden shaped like an equilateral triangle that measures 11 feet on each side. He has placed a watering hose that extends from the faucet located at a vertex to the opposite side, as shown below. Which is closest to the length of the hose in the garden? 26) ΔKLP has vertices K ( 4, 2), L (2, 6), and P (4, 6). It is dilated to form ΔK L P with the origin as the center of dilation. If the coordinates of K are ( 6, 3), what scale factor was used to form ΔK L P? F G H J The numbers represent the lengths of the sides of a triangle. Classify each triangle as acute, obtuse or right: 28. Find x, y and z. 60 a.) 6, 9, 10 b.) 18, 24, 30 c.) 20, 100, Solve for x and y. 30. The diagonal of a square measures 32 meters. What is the area of the square? 31. Mr. Carpenter built a wooden gate, as shown below. Which is closest to the length in feet of the diagonal board that Mr. Carpenter used to brace the wooden gate? 32. If AB ED and AD BE, what is the measure of EB? A 6 m 10 m C B E 25 m D

12 Review for Pre-AP Test 3.4 Cumulative 3 rd Nine-Week Test Name: Date: Period: Review all 3 previous tests in the 3 rd 9-wks! (Proofs will not be on the test.) Give answers in simplest exact form. 1. In quadrilateral ABCD, AB = 5, BC = 17, CD = 2. Find the area and perimeter of the triangle RST. 5, DA = 9. What inequality best describes the range of lengths for BD? If BD is an integer, what is BD? 3. Find the area and perimeter of the rhombus. Leave your answer in simplest radical form. 4. What is the area and perimeter of the non-shaded part of the rectangle below? 100 ft 135º ft Not drawn to scale 5. The lengths of the bases of an isosceles trapezoid are shown below. If the perimeter of this trapezoid is 32 units, what is its area? 6. The top view of the floor of an office building is shown. It consists of part of a circle and two regular polygons. If the radius of the circle is 12 ft. and carpet costs $12 a square yard, $50 for removing the old carpet, and $75 for installing the new carpet, how much would it cost to recarpet the floor? What is the angle measure of the top left vertex? What is the angle measure of the bottom right vertex? 7. Find the area and perimeter of the figure below (a regular hexagon with semicircles attached) AF=FG, and FC=ED=FE=CD. Find the area and perimeter of the figure. A 9 F G 15 B C semicircle E D

13 9. Quadrilateral WXYZ is a parallelogram with WY and XZ intersecting at point E. WX = 2x 1, XY = x + 7, YZ = 6y 5, WZ = 5y + 1. Find WX and WZ. 10. Find the area of the quadrilateral ABCD with coordinates A(-1,5), B(6,4), C(2,-2), D(-5,2). Find new coordinates for D (, ) so that ABCD is a parallelogram. 11. Find the area of the shaded sector? 12. A satellite moves in a nearly circular orbit around Earth, completing an orbit every 24 hours. The radius of the orbit is about 42,000 km. At 1 p.m. the satellite is at point A. At 5 p.m. the satellite is at point B. Approximately how many kilometers does the satellite travel between 1 and 5 p.m.? 13. Doris had a circular garden with a radius of 30 feet. She used all of the fencing from the circular garden to enclose a square garden. What was the approximate length of each side of Doris s square garden? 14. The area of this regular polygon is 72 square inches. Find the approximate length of one side of this polygon (round to the nearest thousandth). 15. A developer wanted to blacktop the shaded portion of this corner building site. How much will it cost if blacktopping costs $5 per square meter? 48 m 16 m 8 m 14 m 16. A city planner measured the distances shown from the old oak, the big rock, and the flag to the east-west line. Other distances along the line are shown. What is the area of the city park? (Hint: Enclose the park with a rectangle.) Big Rock Flag Old Oak City Park 164 m 126 m 83 m 17. The shorter diagonal of a rhombus has the same length as a side. Find the area if the longer diagonal is 12 cm. long. W 62 m 48 m 106 m 18. Find the total area of the parallelogram. (Hint: Find the area of one triangle first.) E 17

~ 1 ~ Geometry 2 nd Semester Review Find the value for the variable for each of the following situations

~ 1 ~ Geometry 2 nd Semester Review Find the value for the variable for each of the following situations Geometry nd Semester Review 018 Find the value for the variable for each of the following situations. 7. 400 m 1. 7 8. y. 8.9 cm 0 0 9.. 19 6 60 1 11 10. 45 4. 58 5 11. 5. 11 6. 18 1 slide 4.1 meters long

More information

MCA/GRAD Formula Review Packet

MCA/GRAD Formula Review Packet MCA/GRAD Formula Review Packet 1 2 3 4 5 6 The MCA-II / BHS 2 Math Plan GRAD Page 1 of 16 Portions Copyright 2005 by Claude Paradis 8 9 10 12 11 13 14 15 16 1 18 19 20 21 The MCA-II / BHS 2 Math Plan GRAD

More information

NORTH THURSTON PUBLIC SCHOOLS END OF COURSE GEOMETRY PRACTICE TEST. Name: Date:

NORTH THURSTON PUBLIC SCHOOLS END OF COURSE GEOMETRY PRACTICE TEST. Name: Date: NORTH THURSTON PUBLIC SCHOOLS END OF COURSE GEOMETRY PRACTICE TEST Name: Date: Day 1 1. Determine the value of x if ΔABC is equilateral. B 7.5x 6x + 3 A Write your answer on the line. 10x 5 C What is the

More information

Find the perimeter of the figure named and shown. Express the perimeter in the same unit of measure that appears on the given side or sides.

Find the perimeter of the figure named and shown. Express the perimeter in the same unit of measure that appears on the given side or sides. Mth101 Chapter 8 HW Name Find the perimeter of the figure named and shown. Express the perimeter in the same unit of measure that appears on the given side or sides. 1) 1) Rectangle 6 in. 12 in. 12 in.

More information

Name Score Period Date. m = 2. Find the geometric mean of the two numbers. Copy and complete the statement.

Name Score Period Date. m = 2. Find the geometric mean of the two numbers. Copy and complete the statement. Chapter 6 Review Geometry Name Score Period Date Solve the proportion. 3 5 1. = m 1 3m 4 m = 2. 12 n = n 3 n = Find the geometric mean of the two numbers. Copy and complete the statement. 7 x 7? 3. 12

More information

Geometry Review- Chapter Find e, and express your answer in simplest radical form.

Geometry Review- Chapter Find e, and express your answer in simplest radical form. Name: Date: Period: Geometry Review- Chapter 10 1. The diagonal of a rectangle measures 15 cm long, and the width is 10. Find the height of the rectangle and epress your answer in simplest radical form.

More information

Name: Class: Date: c. WZ XY and XW YZ. b. WZ ZY and XW YZ. d. WN NZ and YN NX

Name: Class: Date: c. WZ XY and XW YZ. b. WZ ZY and XW YZ. d. WN NZ and YN NX Class: Date: 2nd Semester Exam Review - Geometry CP 1. Complete this statement: A polygon with all sides the same length is said to be. a. regular b. equilateral c. equiangular d. convex 3. Which statement

More information

PRACTICE PROBLEMS CH 8 and Proofs

PRACTICE PROBLEMS CH 8 and Proofs GEOM PRACTICE PROBLEMS CH 8 and Proofs Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the length of the missing side. The triangle is not drawn to

More information

Final Exam Review. Multiple Choice Identify the choice that best completes the statement or answers the question.

Final Exam Review. Multiple Choice Identify the choice that best completes the statement or answers the question. ( Final Exam Review Multiple hoice Identify the choice that best completes the statement or answers the question. 1. is an isosceles triangle. is the longest side with length. = and =. Find. 4 x + 4 7

More information

Geometry Final Exam Review

Geometry Final Exam Review 1. In the figures find the missing parts. Geometry Final Eam Review 2. In the figures find the missing parts. 3. Tom is trying to put a divider diagonally to separate his animals and his play area. If

More information

Geometry Right Triangles and Trigonometry

Geometry Right Triangles and Trigonometry Geometry Right Triangles and Trigonometry Day Date lass Homework Th 2/16 F 2/17 N: Special Right Triangles & Pythagorean Theorem Right Triangle & Pythagorean Theorem Practice Mid-Winter reak WKS: Special

More information

1. LINE SEGMENTS. a and. Theorem 1: If ABC A 1 B 1 C 1, then. the ratio of the areas is as follows: Theorem 2: If DE//BC, then ABC ADE and 2 AD BD

1. LINE SEGMENTS. a and. Theorem 1: If ABC A 1 B 1 C 1, then. the ratio of the areas is as follows: Theorem 2: If DE//BC, then ABC ADE and 2 AD BD Chapter. Geometry Problems. LINE SEGMENTS Theorem : If ABC A B C, then the ratio of the areas is as follows: S ABC a b c ( ) ( ) ( ) S a b A BC c a a b c and b c Theorem : If DE//BC, then ABC ADE and AD

More information

Pre-Algebra Chapter 9 Spatial Thinking

Pre-Algebra Chapter 9 Spatial Thinking Pre-Algebra Chapter 9 Spatial Thinking SOME NUMBERED QUESTIONS HAVE BEEN DELETED OR REMOVED. YOU WILL NOT BE USING A CALCULATOR FOR PART I MULTIPLE-CHOICE QUESTIONS, AND THEREFORE YOU SHOULD NOT USE ONE

More information

For all questions, E is NOTA, which denotes that none of the above is correct. All diagrams are not drawn to scale. All angles are in degrees.

For all questions, E is NOTA, which denotes that none of the above is correct. All diagrams are not drawn to scale. All angles are in degrees. For all questions, E is NOTA, which denotes that none of the above is correct. All diagrams are not drawn to scale. All angles are in degrees. 1. Given a regular polygon with 20 diagonals, find the measure

More information

Geometry Final Review. Chapter 1. Name: Per: Vocab. Example Problems

Geometry Final Review. Chapter 1. Name: Per: Vocab. Example Problems Geometry Final Review Name: Per: Vocab Word Acute angle Adjacent angles Angle bisector Collinear Line Linear pair Midpoint Obtuse angle Plane Pythagorean theorem Ray Right angle Supplementary angles Complementary

More information

Trigonometric ratios:

Trigonometric ratios: 0 Trigonometric ratios: The six trigonometric ratios of A are: Sine Cosine Tangent sin A = opposite leg hypotenuse adjacent leg cos A = hypotenuse tan A = opposite adjacent leg leg and their inverses:

More information

Section 5.1. Perimeter and Area

Section 5.1. Perimeter and Area Section 5.1 Perimeter and Area Perimeter and Area The perimeter of a closed plane figure is the distance around the figure. The area of a closed plane figure is the number of non-overlapping squares of

More information

Final Exam Review Packet

Final Exam Review Packet Final Exam Review Packet Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the length of the missing side. The triangle is not drawn to scale. 6 8 a.

More information

Int Math 2B EOC FIG Assessment ID: ib C. DE = DF. A. ABE ACD B. A + C = 90 C. C + D = B + E D. A = 38 and C = 38

Int Math 2B EOC FIG Assessment ID: ib C. DE = DF. A. ABE ACD B. A + C = 90 C. C + D = B + E D. A = 38 and C = 38 1 If ΔDEF and ΔJKL are two triangles such that D J, which of the following would be sufficient to prove the triangles are similar? A. DE = EF JK KL B. DE = EF JK JL C. DE = DF JK KL D. DE = DF JK JL 2

More information

Geometry: Hutschenreuter Semester II. Select the best answer for each question. Show expected work. MAKE A SUPPORTING SKETCH!

Geometry: Hutschenreuter Semester II. Select the best answer for each question. Show expected work. MAKE A SUPPORTING SKETCH! Geometry: Hutschenreuter Semester II Review B Name Period Date Select the best answer for each question. Show expected work. MAKE A SUPPORTING SKETCH! 1. A parallelogram has a diagonal of 41 cm and side

More information

Geometry Unit 7 - Notes Right Triangles and Trigonometry

Geometry Unit 7 - Notes Right Triangles and Trigonometry Geometry Unit 7 - Notes Right Triangles and Trigonometry Review terms: 1) right angle ) right triangle 3) adjacent 4) Triangle Inequality Theorem Review topic: Geometric mean a = = d a d Syllabus Objective:

More information

17. The length of a diagonal of a square is 16 inches. What is its perimeter? a. 8 2 in. b in. c in. d in. e in.

17. The length of a diagonal of a square is 16 inches. What is its perimeter? a. 8 2 in. b in. c in. d in. e in. Geometry 2 nd Semester Final Review Name: 1. Pentagon FGHIJ pentagon. 2. Find the scale factor of FGHIJ to KLMNO. 3. Find x. 4. Find y. 5. Find z. 6. Find the scale factor of ABCD to EFGD. 7. Find the

More information

GEOMETRY & MEASUREMENT

GEOMETRY & MEASUREMENT GEOMETRY & MESUREMENT 1 1. The measure for a stud for a wall must be 72. Which of the following studs is allowed? 4 a. 72.7 in b. 72.31 in c. 71.81 in d. 71.2 in 2. t a bolt manufacturing company, 6 bolts

More information

Geometry Honors Final Exam Review June 2018

Geometry Honors Final Exam Review June 2018 Geometry Honors Final Exam Review June 2018 1. Determine whether 128 feet, 136 feet, and 245 feet can be the lengths of the sides of a triangle. 2. Casey has a 13-inch television and a 52-inch television

More information

Show all work for full credit. Do NOT use trig to solve special right triangle problems (half credit).

Show all work for full credit. Do NOT use trig to solve special right triangle problems (half credit). Chapter 8 Retake Review 1 The length of the hypotenuse of a 30 60 90 triangle is 4. Find the perimeter. 2 What similarity statement can you write relating the three triangles in the diagram? 5 Find the

More information

Radicals and Pythagorean Theorem Date: Per:

Radicals and Pythagorean Theorem Date: Per: Math 2 Unit 7 Worksheet 1 Name: Radicals and Pythagorean Theorem Date: Per: [1-12] Simplify each radical expression. 1. 75 2. 24. 7 2 4. 10 12 5. 2 6 6. 2 15 20 7. 11 2 8. 9 2 9. 2 2 10. 5 2 11. 7 5 2

More information

Geometry Final Exam 2014 Study Guide. Name Date Block

Geometry Final Exam 2014 Study Guide. Name Date Block Geometry Final Exam 014 Study Guide Name Date Block The final exam for Geometry will take place on June 5. The following study guide will help you prepare for the exam. Everything we have covered is fair

More information

A. 180 B. 108 C. 360 D. 540

A. 180 B. 108 C. 360 D. 540 Part I - Multiple Choice - Circle your answer: 1. Find the area of the shaded sector. Q O 8 P A. 2 π B. 4 π C. 8 π D. 16 π 2. An octagon has sides. A. five B. six C. eight D. ten 3. The sum of the interior

More information

Geometry Warm Up Right Triangles Day 8 Date

Geometry Warm Up Right Triangles Day 8 Date Geometry Warm Up Right Triangles Day 8 Name Date Questions 1 4: Use the following diagram. Round decimals to the nearest tenth. P r q Q p R 1. If PR = 12 and m R = 19, find p. 2. If m P = 58 and r = 5,

More information

221 MATH REFRESHER session 3 SAT2015_P06.indd 221 4/23/14 11:39 AM

221 MATH REFRESHER session 3 SAT2015_P06.indd 221 4/23/14 11:39 AM Math Refresher Session 3 1 Area, Perimeter, and Volume Problems Area, Perimeter, and Volume 301. Formula Problems. Here, you are given certain data about one or more geometric figures, and you are asked

More information

Prerequisite Skills. y x =

Prerequisite Skills. y x = Prerequisite Skills BLM 1 1... Solve Equations 1. Solve. 2x + 5 = 11 x 5 + 6 = 7 x 2 = 225 d) x 2 = 24 2 + 32 2 e) 60 2 + x 2 = 61 2 f) 13 2 12 2 = x 2 The Pythagorean Theorem 2. Find the measure of the

More information

Geometry Final Exam REVIEW

Geometry Final Exam REVIEW Name: Class: _ Date: _ Geometry Final Exam 09-10 - REVIEW Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the perimeter and area of the parallelogram.

More information

T.4 Applications of Right Angle Trigonometry

T.4 Applications of Right Angle Trigonometry 424 section T4 T.4 Applications of Right Angle Trigonometry Solving Right Triangles Geometry of right triangles has many applications in the real world. It is often used by carpenters, surveyors, engineers,

More information

+ 10 then give the value

+ 10 then give the value 1. Match each vocabulary word to the picture. A. Linear Pair B. Vertical Angles P1 C. Angle Bisector D. Parallel Lines E. Orthocenter F. Centroid For questions 3 4 use the diagram below. Y Z X U W V A

More information

Pre-Test. Use trigonometric ratios to find the value of x. Show all your work and round your answer to the nearest tenth.

Pre-Test. Use trigonometric ratios to find the value of x. Show all your work and round your answer to the nearest tenth. Pre-Test Name Date 1. Write the trigonometric ratios for A. Write your answers as simplified fractions. A 6 cm 10 cm sin A cos A 8 10 5 6 10 3 5 C 8 cm B tan A 8 6 3 2. Write the trigonometric ratios for

More information

Trigonometry Applications

Trigonometry Applications Name: Date: Period Trigonometry Applications Draw a picture (if one is not provided), write an equation, and solve each problem. Round answers to the nearest hundredths. 1. A 110-ft crane set at an angle

More information

CHAPTER 12 HERON S FORMULA Introduction

CHAPTER 12 HERON S FORMULA Introduction CHAPTER 1 HERON S FORMULA 1.1 Introduction You have studied in earlier classes about figures of different shapes such as squares, rectangles, triangles and quadrilaterals. You have also calculated perimeters

More information

Math 1201 Review Chapter 2

Math 1201 Review Chapter 2 Math 1201 Review hapter 2 Multiple hoice Identify the choice that best completes the statement or answers the question. 1. etermine tan Q and tan R. P 12 Q 16 R a. tan Q = 0.428571; tan R = 0.75 c. tan

More information

Context-Based Multiple-Choice Questions

Context-Based Multiple-Choice Questions UNIT3 Chapters BUILDING 8 10 Strategies for Answering Context-Based Multiple-Choice Questions Some of the information you need to solve a context-based multiple-choice question may appear in a table, a

More information

Squares and Square Roots. The Pythagorean Theorem. Similar Figures and Indirect Measurement

Squares and Square Roots. The Pythagorean Theorem. Similar Figures and Indirect Measurement Lesson 9-1 Lesson 9-2 Lesson 9-3 Lesson 9-4 Lesson 9-5 Lesson 9-6 Squares and Square Roots The Real Number System Triangles The Pythagorean Theorem The Distance Formula Similar Figures and Indirect Measurement

More information

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Math 1332 Chapter 10 Review Name Solve the problem. 1) The hour hand of a clock moves from 12 to 4 oʹclock. Through how many degrees does it move? 1) Find the measure of the angle in which? appears. 2)

More information

Indicate whether the statement is true or false.

Indicate whether the statement is true or false. PRACTICE EXAM IV Sections 6.1, 6.2, 8.1 8.4 Indicate whether the statement is true or false. 1. For a circle, the constant ratio of the circumference C to length of diameter d is represented by the number.

More information

b) Parallelogram Opposite Sides Converse c) Parallelogram Diagonals Converse d) Opposite sides Parallel and Congruent Theorem

b) Parallelogram Opposite Sides Converse c) Parallelogram Diagonals Converse d) Opposite sides Parallel and Congruent Theorem Chapter 7 1. State which theorem you can use to show that the quadrilateral is a parallelogram. a) Parallelogram Opposite Angles Converse b) Parallelogram Opposite Sides Converse c) Parallelogram Diagonals

More information

4.! ABC ~ DEF,! AC = 6 ft, CB = 3 ft, AB = 7 ft, DF = 9 ft.! What is the measure of EF?

4.! ABC ~ DEF,! AC = 6 ft, CB = 3 ft, AB = 7 ft, DF = 9 ft.! What is the measure of EF? Name:!!!!!!!!!!!!! Geo(2) GEOMETRY (2) REVIEW FOR FINAL EXAM #2 1. If ABC is similar to ADE, then AB AD =? AE. Which replaces the? to make the statement true? A. AC!! B. AE!! C. DE!! D. BC 2. In ABC,

More information

Objective 8 - Page 1 of 6

Objective 8 - Page 1 of 6 Objective 8 - Page of 6 The drama department at McHenry High School has built a stage floor in the shape of a regular octagon. The length of each side of the octagon is 4 yards. is the apothem. What is

More information

Kansas City Area Teachers of Mathematics 2013 KCATM Math Competition GEOMETRY GRADES 7-8

Kansas City Area Teachers of Mathematics 2013 KCATM Math Competition GEOMETRY GRADES 7-8 Kansas City Area Teachers of Mathematics 2013 KCATM Math Competition GEOMETRY GRADES 7-8 INSTRUCTIONS Do not open this booklet until instructed to do so. Time limit: 20 minutes You may use calculators.

More information

1.1 Angles, Degrees, and Arcs

1.1 Angles, Degrees, and Arcs MA140 Trig 2015 Homework p. 1 Name: 1.1 Angles, Degrees, and Arcs Find the fraction of a counterclockwise revolution that will form an angle with the indicated number of degrees. 3(a). 45 3(b). 150 3(c).

More information

The Theorem of Pythagoras

The Theorem of Pythagoras CONDENSED LESSON 9.1 The Theorem of Pythagoras In this lesson you will Learn about the Pythagorean Theorem, which states the relationship between the lengths of the legs and the length of the hypotenuse

More information

Geometry Unit 8 - Notes Perimeter and Area

Geometry Unit 8 - Notes Perimeter and Area Geometry Unit 8 - Notes Perimeter and Area Syllabus Objective: 8. - The student will formulate strategies for finding the perimeter or area of various geometric figures. Review terms: ) area ) perimeter

More information

Geometry Cumulative Review

Geometry Cumulative Review Geometry Cumulative Review Name 1. Find a pattern for the sequence. Use the pattern to show the next term. 1, 3, 9, 27,... A. 81 B. 45 C. 41 D. 36 2. If EG = 42, find the value of y. A. 5 B. C. 6 D. 7

More information

ACT Test Prep. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

ACT Test Prep. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question. Name: Class: Date: ID: A ACT Test Prep Multiple Choice Identify the choice that best completes the statement or answers the question.. 80 is % of what number? 8 d. 00 0 0. Solve ( 8 x) = 6x +. d.. The

More information

Chapter 7 Sect. 2. A pythagorean triple is a set of three nonzero whole numbers a, b, and c, that satisfy the equation a 2 + b 2 = c 2.

Chapter 7 Sect. 2. A pythagorean triple is a set of three nonzero whole numbers a, b, and c, that satisfy the equation a 2 + b 2 = c 2. Chapter 7 Sect. 2 The well-known right triangle relationship called the Pythagorean Theorem is named for Pythagoras, a Greek mathematician who lived in the sixth century b.c. We now know that the Babylonians,

More information

Answers. Investigation 4. ACE Assignment Choices. Applications. The number under the square root sign increases by 1 for every new triangle.

Answers. Investigation 4. ACE Assignment Choices. Applications. The number under the square root sign increases by 1 for every new triangle. Answers Investigation 4 ACE Assignment Choices Problem 4. Core, Other Connections 6 Problem 4. Core, 4, Other Applications 6 ; Connections 7, 6, 7; Extensions 8 46; unassigned choices from earlier problems

More information

ALGEBRA I AND GEOMETRY SUMMER ASSIGNMENT

ALGEBRA I AND GEOMETRY SUMMER ASSIGNMENT NAME: This packet has been designed to help you review various mathematical topics that are necessary for your success in Algebra I and/or Geometry next year, as well as PSAT/SAT/ACT. Complete all problems

More information

9.3. Practice C For use with pages Tell whether the triangle is a right triangle.

9.3. Practice C For use with pages Tell whether the triangle is a right triangle. LESSON 9.3 NAME DATE For use with pages 543 549 Tell whether the triangle is a right triangle. 1. 21 2. 3. 75 6 2 2 17 72 63 66 16 2 4. 110 5. 4.3 6. 96 2 4.4 10 3 3 4.5 Decide whether the numbers can

More information

Geometry. Midterm Review

Geometry. Midterm Review Geometry Midterm Review Class: Date: Geometry Midterm Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1 A plumber knows that if you shut off the water

More information

4. Solve for x: 5. Use the FOIL pattern to multiply (4x 2)(x + 3). 6. Simplify using exponent rules: (6x 3 )(2x) 3

4. Solve for x: 5. Use the FOIL pattern to multiply (4x 2)(x + 3). 6. Simplify using exponent rules: (6x 3 )(2x) 3 SUMMER REVIEW FOR STUDENTS COMPLETING ALGEBRA I WEEK 1 1. Write the slope-intercept form of an equation of a. Write a definition of slope. 7 line with a slope of, and a y-intercept of 3. 11 3. You want

More information

Math Self-Test Version Form A Measurement and Geometry

Math Self-Test Version Form A Measurement and Geometry Math Self-Test Version 0.1.1 Form A Measurement and Geometry Draw each object and describe the key characteristics that define the object. [3 pts. each] 1) Acute Triangle 2) Arc 3) Chord 4) Cube 5) Cylinder

More information

Ch6prac 1.Find the degree measure of the angle with the given radian measure. (Round your answer to the nearest whole number.) -2

Ch6prac 1.Find the degree measure of the angle with the given radian measure. (Round your answer to the nearest whole number.) -2 Ch6prac 1.Find the degree measure of the angle with the given radian measure. (Round your answer to the nearest whole number.) -2 2. Find the degree measure of the angle with the given radian measure.

More information

Accelerated Math 7 Second Semester Final Practice Test

Accelerated Math 7 Second Semester Final Practice Test Accelerated Math 7 Second Semester Final Practice Test Name Period Date Part 1 Learning Target 5: I can solve problems applying scale factor to geometric figures or scale drawings. 1. What is the value

More information

Math 5 Trigonometry Fair Game for Chapter 1 Test Show all work for credit. Write all responses on separate paper.

Math 5 Trigonometry Fair Game for Chapter 1 Test Show all work for credit. Write all responses on separate paper. Math 5 Trigonometry Fair Game for Chapter 1 Test Show all work for credit. Write all responses on separate paper. 12. What angle has the same measure as its complement? How do you know? 12. What is the

More information

Geometry Honors Homework

Geometry Honors Homework Geometry Honors Homework pg. 1 12-1 Practice Form G Tangent Lines Algebra Assume that lines that appear to be tangent are tangent. O is the center of each circle. What is the value of x? 1. 2. 3. The circle

More information

CHAPTER 11 AREAS OF PLANE FIGURES

CHAPTER 11 AREAS OF PLANE FIGURES CHAPTER 11 AREAS OF PLANE FIGURES EXERCISE 45, Page 106 1. Find the angles p and q in diagram (a) below. p = 180-75 = 105 (interior opposite angles of a parallelogram are equal) q = 180-105 - 40 = 35.

More information

Practice Lesson 11-1 Practice Algebra 1 Chapter 11 "256 "32 "96. "65 "2a "13. "48n. "6n 3 "180. "25x 2 "48 "10 "60 "12. "8x 6 y 7.

Practice Lesson 11-1 Practice Algebra 1 Chapter 11 256 32 96. 65 2a 13. 48n. 6n 3 180. 25x 2 48 10 60 12. 8x 6 y 7. Practice 11-1 Simplifying Radicals Simplify each radical epression. 1. "32 2. "22? "8 3. "147 4. 17 5. "a 2 b 5 Ä 144 6. 2 "256 7. "80 8. "27 9. 10. 8 "6 "32 "7 "96 11. "12 4 12. 13. "200 14. 12 15. "15?

More information

Day 6: Angles of Depression and Elevation. Unit 5: Trigonometric Functions

Day 6: Angles of Depression and Elevation. Unit 5: Trigonometric Functions + Day 6: Angles of Depression and Elevation Unit 5: Trigonometric Functions Warm Up + n Find the missing side length 1) 2) n Find the missing angle 10 minutes 3) 4) End + Homework Check + Today s Objective

More information

1 What is the solution of the system of equations graphed below? y = 2x + 1

1 What is the solution of the system of equations graphed below? y = 2x + 1 1 What is the solution of the system of equations graphed below? y = 2x + 1 3 As shown in the diagram below, when hexagon ABCDEF is reflected over line m, the image is hexagon A'B'C'D'E'F'. y = x 2 + 2x

More information

Quadratic Word Problems - Develop an Approach and Solve

Quadratic Word Problems - Develop an Approach and Solve Name: Class: Date: ID: A Quadratic Word Problems - Develop an Approach and Solve Short Answer 1. Suppose you have 54 feet of fencing to enclose a rectangular dog pen. The function A = 7x x, where x = width,

More information

Practice Test Student Answer Document

Practice Test Student Answer Document Practice Test Student Answer Document Record your answers by coloring in the appropriate bubble for the best answer to each question. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

More information

Park School Mathematics Curriculum Book 3, Lesson 3: Trig and Shapes

Park School Mathematics Curriculum Book 3, Lesson 3: Trig and Shapes Park School Mathematics Curriculum Book 3, Lesson 3: Trig and Shapes We re providing this lesson as a sample of the curriculum we use at the Park School of Baltimore in grades 9-11. If you d like to know

More information

Geometry GT/Honors 3 rd 9 weeks Homework Answers

Geometry GT/Honors 3 rd 9 weeks Homework Answers School holiday winter break. Geometry GT/Honors rd 9 weeks Homework Answers Monday Tuesday Wednesday Thursday Friday School holiday winter break. Finish notes/classwork on Inequalities in Triangles. Ex:

More information

Unit 2 Review. Determine the scale factor of the dilation below.

Unit 2 Review. Determine the scale factor of the dilation below. Unit 2 Review 1. oes the graph below represent a dilation? Why or why not? y 10 9 8 7 (0, 7) 6 5 4 3 (0, 3.5) 2 1 (5, 7) (5, 3.5) -10-9 -8-7 -6-5 -4-3 -2-1 0 1 2 3 4 5 6 7 8 9 10-1 F -2 (5, 0) -3-4 -5-6

More information

Chapter 8. Chapter 8 Opener. Section 8.1. Big Ideas Math Red Accelerated Worked-Out Solutions 4 7 = = 4 49 = = 39 = = 3 81 = 243

Chapter 8. Chapter 8 Opener. Section 8.1. Big Ideas Math Red Accelerated Worked-Out Solutions 4 7 = = 4 49 = = 39 = = 3 81 = 243 Chapter 8 Opener Try It Yourself (p. 35). trapezoids. circles Large Perimeter Diameter Small Perimeter Diameter Average of Ratios 3. trapezoid, triangle. triangles 5. rectangle, triangle 6. rectangle,

More information

Polynomials 370 UNIT 10 WORKING WITH POLYNOMIALS. The railcars are linked together.

Polynomials 370 UNIT 10 WORKING WITH POLYNOMIALS. The railcars are linked together. UNIT 10 Working with Polynomials The railcars are linked together. 370 UNIT 10 WORKING WITH POLYNOMIALS Just as a train is built from linking railcars together, a polynomial is built by bringing terms

More information

0611ge. Geometry Regents Exam Line segment AB is shown in the diagram below.

0611ge. Geometry Regents Exam Line segment AB is shown in the diagram below. 0611ge 1 Line segment AB is shown in the diagram below. In the diagram below, A B C is a transformation of ABC, and A B C is a transformation of A B C. Which two sets of construction marks, labeled I,

More information

#12 Algebra 2 Notes Using Trig in Real Life

#12 Algebra 2 Notes Using Trig in Real Life #12 Algebra 2 Notes 13.1 Using Trig in Real Life #12 Algebra 2 Notes: 13.1 using Trig in Real Life Angle of Elevation Angle of Elevation means you are looking upward and is usually measured from the ground

More information

Name: Class: Date: Use a trigonometric ratio to determine the value of x. Round your answer to the nearest tenth.

Name: Class: Date: Use a trigonometric ratio to determine the value of x. Round your answer to the nearest tenth. Class: Date: Ch 9 Questions 1. Use a trigonometric ratio to determine the value of x. Round your answer to the nearest tenth. 2. 3. 4. Estimate m X to the nearest degree. 5. Katie and Matt are both flying

More information

Geometric Formulas (page 474) Name

Geometric Formulas (page 474) Name LESSON 91 Geometric Formulas (page 474) Name Figure Perimeter Area Square P = 4s A = s 2 Rectangle P = 2I + 2w A = Iw Parallelogram P = 2b + 2s A = bh Triangle P = s 1 + s 2 + s 3 A = 1_ 2 bh Teacher Note:

More information

SOL Review Items. 7.1 The student will. 7.1a 1. Which fraction and decimal are equivalent to A. and B. and C. and D. and 0.

SOL Review Items. 7.1 The student will. 7.1a 1. Which fraction and decimal are equivalent to A. and B. and C. and D. and 0. 7.1 The student will a) investigate and describe the concept of negative exponents for powers of ten; b) determine scientific notation for numbers greater than zero; c) compare and order fractions, decimals,

More information

Accelerated Geometry/Algebra 2 Summer Math Packet. Student Information Page

Accelerated Geometry/Algebra 2 Summer Math Packet. Student Information Page Student Information Page We re so proud of you for taking the time to work on math over the summer! Here are some helpful hints for success: It s ok to have parents and other adults help you! Find a quiet

More information

Expressions and the Number System

Expressions and the Number System Name: 8 th Grade Math 1 st Semester Review Pd: Expressions and the Number System 1. A square rug has an area of 225 square feet. How long is each side of the rug? A 15 feet B 22.5 feet C 23 feet D 25 feet

More information

Course End Review Grade 10: Academic Mathematics

Course End Review Grade 10: Academic Mathematics Course End Review Grade 10: Academic Mathematics Linear Systems: 1. For each of the following linear equations place in y = mx + b format. (a) 3 x + 6y = 1 (b) 4 x 3y = 15. Given 1 x 4y = 36, state: (a)

More information

OVERVIEW Use Trigonometry & Pythagorean Theorem to Solve G.SRT.8

OVERVIEW Use Trigonometry & Pythagorean Theorem to Solve G.SRT.8 OVERVIEW Use Trigonometry & Pythagorean Theorem to Solve G.SRT.8 G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. No surprises here. Use trigonometry

More information

Find the side length of each square tile. Use a complete sentence to explain how you found your answer cm 2

Find the side length of each square tile. Use a complete sentence to explain how you found your answer cm 2 Assignment Assignment for Lesson.1 Name Date Tiling a Bathroom Wall Simplifying Square Root Expressions Find the side length of each square tile. Use a complete sentence to explain how you found your answer.

More information

Chapter 7: Practice/review problems The collection of problems listed below contains questions taken from previous MA123 exams.

Chapter 7: Practice/review problems The collection of problems listed below contains questions taken from previous MA123 exams. Word problems Chapter 7: Practice/review problems The collection of problems listed below contains questions taken from previous MA3 exams. Max-min problems []. A field has the shape of a rectangle with

More information

UNCC 2001 Comprehensive, Solutions

UNCC 2001 Comprehensive, Solutions UNCC 2001 Comprehensive, Solutions March 5, 2001 1 Compute the sum of the roots of x 2 5x + 6 = 0 (A) (B) 7/2 (C) 4 (D) 9/2 (E) 5 (E) The sum of the roots of the quadratic ax 2 + bx + c = 0 is b/a which,

More information

Be prepared to find the volume, area, and volume of any of the shapes covered in lecture and/or homework. A rhombus is also a square.

Be prepared to find the volume, area, and volume of any of the shapes covered in lecture and/or homework. A rhombus is also a square. Math 254SI Practice Problem Set 5 (Chapter 8&9) Do these problems on a separate piece of paper(s). Remember that the quiz is closed book and closed notes except for the Geometry handout that I will provide.

More information

Geometry Module 5 Unit 1 Practice Exam

Geometry Module 5 Unit 1 Practice Exam Name: Class: Date: Geometry Module 5 Unit 1 Practice Exam Short Answer 1. What are the minor arcs of O? 2. What are the major arcs of O that contain point M? 3. Identify a semicircle that contains C. 1

More information

Test Review: Geometry I Period 3,5,7. ASSESSMENT DATE: Wednesday 3/25 (FOR ALL CLASSES) Things it would be a good idea to know:

Test Review: Geometry I Period 3,5,7. ASSESSMENT DATE: Wednesday 3/25 (FOR ALL CLASSES) Things it would be a good idea to know: Test Review: Geometry I Period 3,5,7 ASSESSMENT DATE: Wednesday 3/25 (FOR ALL CLASSES) Things it would be a good idea to know: 1) How to create proportions from a. a word problem b. a pair of similar triangles

More information

Find the length of an arc that subtends a central angle of 45 in a circle of radius 8 m. Round your answer to 3 decimal places.

Find the length of an arc that subtends a central angle of 45 in a circle of radius 8 m. Round your answer to 3 decimal places. Chapter 6 Practice Test Find the radian measure of the angle with the given degree measure. (Round your answer to three decimal places.) 80 Find the degree measure of the angle with the given radian measure:

More information

Standardized Test Practice - Cumulative, Chapters What is the value of x in the figure below?

Standardized Test Practice - Cumulative, Chapters What is the value of x in the figure below? 1. What is the value of x in the figure below? 2. A baseball diamond is a square with 90-ft sides. What is the length from 3rd base to 1st base? Round to the nearest tenth. A 22.5 B 23 C 23.5 D 24 Use

More information

Geometry review two. Name: Class: Date: Multiple Choice Identify the letter of the choice that best completes the statement or answers the question.

Geometry review two. Name: Class: Date: Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. Name: Class: Date: Geometr review two Multiple Choice Identif the letter of the choice that best completes the statement or answers the question. 1. If a b = 5, then 3a =. 3 2. a. 3b b. 10b c. 5b d. 6b

More information

Days 3 & 4 Notes: Related Rates

Days 3 & 4 Notes: Related Rates AP Calculus Unit 4 Applications of the Derivative Part 1 Days 3 & 4 Notes: Related Rates Implicitly differentiate the following formulas with respect to time. State what each rate in the differential equation

More information

SUMMER WORK 2017 Name:

SUMMER WORK 2017 Name: SUMMER WORK 2017 Name: SUMMER WORK is due at the beginning of class on the FIRST DAY OF SCHOOL. It is graded! Welcome to Accelerated GSE Geometry B/Algebra II at Whitewater High School. We are excited

More information

Geometry Simulation Test 2014 Region 1

Geometry Simulation Test 2014 Region 1 Geometry Simulation Test 2014 Region 1 1 etermine the inverse of Mark Twain s quote If you tell the truth, you don t have to remember anything. You don t have to remember anything if you tell the truth.

More information

Park Forest Math Team. Meet #4. Geometry. Self-study Packet

Park Forest Math Team. Meet #4. Geometry. Self-study Packet Park Forest Math Team Meet #4 Self-study Packet Problem Categories for this Meet: 1. Mystery: Problem solving 2. : ngle measures in plane figures including supplements and complements 3. Number Theory:

More information

Gauss School and Gauss Math Circle 2017 Gauss Math Tournament Grade 7-8 (Sprint Round 50 minutes)

Gauss School and Gauss Math Circle 2017 Gauss Math Tournament Grade 7-8 (Sprint Round 50 minutes) Gauss School and Gauss Math Circle 2017 Gauss Math Tournament Grade 7-8 (Sprint Round 50 minutes) 1. Compute. 2. Solve for x: 3. What is the sum of the negative integers that satisfy the inequality 2x

More information

Set up equations to find the lengths of the sides labeled by variables, and Find answers to the equations x. 19 y a a b.

Set up equations to find the lengths of the sides labeled by variables, and Find answers to the equations x. 19 y a a b. SHADOWS After Day 10 SIMILAR POLYGONS In each of the pairs of figures below, assume the figures are similar and that they are facing the same way; that is, assume that the left side of one corresponds

More information

5-10 Indirect Measurement

5-10 Indirect Measurement 1. A basketball hoop in Miguel s backyard casts a shadow that is 8 feet long. At the same time, Miguel casts a shadow that is 4.5 feet long. If Miguel is 5.5 feet tall, how tall is the basketball hoop?

More information

Geometer: CPM Chapters 1-6 Period: DEAL. 7) Name the transformation(s) that are not isometric. Justify your answer.

Geometer: CPM Chapters 1-6 Period: DEAL. 7) Name the transformation(s) that are not isometric. Justify your answer. Semester 1 Closure Geometer: CPM Chapters 1-6 Period: DEAL Take time to review the notes we have taken in class so far and previous closure packets. Look for concepts you feel very comfortable with and

More information