Solving Proportions: Find x: 4 x = x. 2 = x x = 3x. 5 = 3x x = x 3 = 3 x. x =

Size: px
Start display at page:

Download "Solving Proportions: Find x: 4 x = x. 2 = x x = 3x. 5 = 3x x = x 3 = 3 x. x ="

Transcription

1 Similar Triangles Page 1 Solving Proportions: Find x: 1. 4 x = x 2 = x + 4 x = 3x 2x 4. 7 x 5 = 3x x = x 3 = 3 x 7. x = x = ircle the true proportions:. 6 8 = = = 14 21

2 Similar Triangles Page 2 Find x (not all of the following are proportions): 1. x 3 + 5x 6 =1 2. x + 2 x + 3 = x +1 4x 1 = x 7 x 3 = x 5 + x 6 = 1 2x 1 6. = x x 5 = x x 8 = 2 x 9. 4x x 6 4 = 2x x = 2x 1 3

3 Similar Triangles Page 3 1. Reduce the following ratio: 2. Reduce the following ratio: x 2 3x 40 x 2 + 6x x 2 96x x 2 80x Solve for x: 4. Solve for x: 5. Solve for x: x +1 x + 3 = 2 x 2x 2 = 3x 5 3x 3 x 9 = 3 x 6. Solve for x and y: 7. Solve for x and y: 3x + 2 = 5y y 6x = y 2x = x +11 = y Find the ratio of y to x and find the ratio of x to y if 3y ax = 2x + by. 9. Find x:y and y:x if 3 x + y = 5 y x 10. Find x:y and y:x if 6 x + 3 = 12 y If 10y=4x, find x:y 12. If ax cy=dy+bx find y x

4 Similar Triangles Page Show that a b = c d is equivalent to a c = a + b c + d 14. (ST: May 1997) 15. (ST: November 1996) If 10 a = b 12, what is the value of ab? If x y = 1, then x +y = 16. (ST: March 1994) In 1980, the ratio of male students to female students at Frost ollege was 2 males to 3 females. Since then, the enrollment of male students in the college has increased by 400 and the enrollment of female students has remained the same. The ratio of males to females is currently 1 to 1. How many students are currently enrolled at Frost ollege? 17. (ST: May 1996) If the ratio of q to r is 4 to 5, which of the following could be true? a. q = 0, r = 4 5 b. q = 2, r = 5 c. q = 5, r = 6 2 d. q = 15, r = 12 e. q = 16, r = (ST: January 1997) If x = 2y, y = 4z, 2z = w, and w 0, then what is x w?

5 Similar Triangles Page 5 1. JKL ~ Similar Triangles. Which angles are equal?. Which sides are proportional? 2. R ~ GL Mark the equal angles R 7 G L. Find L. Find GL 3. WN ~ T Mark the equal angles. N W 12 T. Find T.. Find T

6 Similar Triangles Page Find UK.. Find N. 5. = and = F. Therefore, ~ by theorem. Find x. = 2x 18, F = 4, = 5, = x F

7 Similar Triangles Page 7 6. ~ F Mark the equal angles. Find x. = 3, F = 4, = x, = 68 F 7. RG ~ UP U 2x+2 4x 2 R 6 G 9 P. Find R.. Find U

8 Similar Triangles Page 8 8) a. In the diagram below, Δ : Δ b. Find c. Find the coordinates of ( 9, 44) (1, 20) (0, 0) (6, 8) 9) Find x and y. 5

9 Similar Triangles Page 9 1. When a line is parallel to one side of a triangle it:. uts the sides proportionally.. Forms a small triangle similar to the large one. omplete the following proportions:. =. =. =. =. = F. = 2. Solve for x: = 16, = x, = 4, = 3

10 Similar Triangles Page Solve for x: = 3, = 4, = x + 5, = x + 10, 4. Solve for x: = 2, = 3, = x + 4, = x + 10,. 5. Solve for x: = 5, = 2, = x + 6, = x 6

11 Similar Triangles Page Solve for x: = 3, = 4, = x 6, = x + 6,. 7. Solve for x: = 5, = 2, = 3x + 6, = 5x Find the value of x: x

12 Similar Triangles Page 12 The Similarity Theorem For any two triangles, if two pairs of corresponding angles are equal, then the triangles are similar. PQR ~ R Q P 1. Which pairs of triangles are similar by the Theorem?

13 Similar Triangles Page 13 Using the Theorem to find the lengths of sides of triangles. 1. In RST, GH RS, RS = 18, GH = 6 and GT = 9. S G R H T. = ecause:. = ecause:. ~ by the Theorem. Find ST. 2. In TR and MSR, T SM, T = 21, SM = 14 and TR = 18. T S R M. = ecause:. = ecause:. ~ by the Theorem. Find MR.

14 Similar Triangles Page Which pairs of triangles are similar by the Theorem? rod 3 meters tall casts a shadow 5 meters long. t the same time, the shadow of a tower is 110 meters long. The sun s rays form equal angles with both the tower and the rod. P x 3 R 110 Q 5 How tall is the tower?

15 Similar Triangles Page Q Two olumn Statement Reason Proofs with Similar Triangles R T Given: PQ ST Prove; PQR ~ TSR S P Statement Reason 1. PQ ST Q = S P = T PQR ~ TSR X O Given: XY ~ O Prove: O ~ O Y Statement Reason 1. XY ~ O = O = O3. 4. O ~ O 4.

16 Similar Triangles Page Given: bisects = Prove: ~ Statement Reason Given: = F = F Prove: F ~ F F Statement Reason

17 Similar Triangles Page 17 pplying ratios and proportions to word problems 1. Susan and ebbie were building a model plane with a scale of 2:143. a. When they were done, they measured the model and found that it was 23 in long. They then calculated the length of the real plane and found that it was ft long. b. Susan and ebbie lost their ruler and they could not measure their model s wingspan. The box that the model had come in said that the real plane had a wingspan of 49 ft, so Susan and ebbie figured out that their model had to have a wingspan of inches. 2. The ratio of males to females in a room is 2 to 3. If there are 625 people total in the room, how many males are there? 3. dog and a puppy together weigh 56 pounds with the ratio of their weights being 5 to 2. How much does the puppy weigh? 4. The sides a, b and c of a triangle correspond, respectively to the sides r, s and t of a similar triangle. Find the length of side t in terms of b, c and s. 5. Δ : ΔXYZ with =5, =7, and =10. The perimeter of ΔXYZ is 33. Find the length of the longest side of ΔXYZ.

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

Geometry L2 Test Review Packet Similarity Test Date Friday March 18 Review Date Thursday March 17. Things it would be a good idea to know

Geometry L2 Test Review Packet Similarity Test Date Friday March 18 Review Date Thursday March 17. Things it would be a good idea to know Geometry L2 Test Review Packet Similarity Test Date Friday March 18 Review Date Thursday March 17 Things it would be a good idea to know 1. How to create a proportion from a. a word problem b. a pair of

More information

Inside Out. Triangle Sum, Exterior Angle, and Exterior Angle Inequality Theorems. Lesson 3.1 Assignment

Inside Out. Triangle Sum, Exterior Angle, and Exterior Angle Inequality Theorems. Lesson 3.1 Assignment Lesson.1 Assignment Name Date Inside Out Triangle Sum, Exterior Angle, and Exterior Angle Inequality Theorems 1. Determine the measure of angle UPM in the figure shown. Explain your reasoning and show

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

~ 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

Over Lesson 7 2 Determine whether the triangles are similar. The quadrilaterals are similar. Find the scale factor of the larger quadrilateral to the

Over Lesson 7 2 Determine whether the triangles are similar. The quadrilaterals are similar. Find the scale factor of the larger quadrilateral to the Five-Minute Check (over Lesson 7 2) CCSS Then/Now Postulate 7.1: Angle-Angle (AA) Similarity Example 1: Use the AA Similarity Postulate Theorems Proof: Theorem 7.2 Example 2: Use the SSS and SAS Similarity

More information

GEOMETRY Teacher: Mrs. Flynn Topic: Similarity. Teacher: Mrs. Flynn Topic: Similarity

GEOMETRY Teacher: Mrs. Flynn Topic: Similarity. Teacher: Mrs. Flynn Topic: Similarity GEOMETRY Teacher: Mrs. Flynn Topic: Similarity Name: Date: Teacher: Mrs. Flynn Topic: Similarity 1. A tree casts a shadow 24 feet long at the same time a man 6 feet tall casts a shadow 4 feet long. Find

More information

Solutions to the Olympiad Maclaurin Paper

Solutions to the Olympiad Maclaurin Paper s to the Olympiad Maclaurin Paper M1. The positive integer N has five digits. The six-digit integer Pis formed by appending the digit 2 to the front of N. The six-digit integer Q is formed by appending

More information

Express g(x) in the form f(x) + ln a, where a (4)

Express g(x) in the form f(x) + ln a, where a (4) SL 2 SUMMER PACKET PRINT OUT ENTIRE PACKET, SHOW YOUR WORK FOR ALL EXERCISES ON SEPARATE PAPER. MAKE SURE THAT YOUR WORK IS NEAT AND ORGANIZED. WORK SHOULD BE COMPLETE AND READY TO TURN IN THE FIRST DAY

More information

Foundation of Math II - Practice Exam

Foundation of Math II - Practice Exam Name: Date: Foundation of Math II - Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. Write your answer in the blank on the left of the number!!

More information

Which statement is true about parallelogram FGHJ and parallelogram F ''G''H''J ''?

Which statement is true about parallelogram FGHJ and parallelogram F ''G''H''J ''? Unit 2 Review 1. Parallelogram FGHJ was translated 3 units down to form parallelogram F 'G'H'J '. Parallelogram F 'G'H'J ' was then rotated 90 counterclockwise about point G' to obtain parallelogram F

More information

Express g(x) in the form f(x) + ln a, where a (4)

Express g(x) in the form f(x) + ln a, where a (4) SL 2 SUMMER PACKET 2013 PRINT OUT ENTIRE PACKET, SHOW YOUR WORK FOR ALL EXERCISES ON SEPARATE PAPER. MAKE SURE THAT YOUR WORK IS NEAT AND ORGANIZED. WORK SHOULD BE COMPLETE AND READY TO TURN IN THE FIRST

More information

Free Pre-Algebra Lesson 59! page 1

Free Pre-Algebra Lesson 59! page 1 Free Pre-Algebra Lesson 59! page 1 Lesson 59: Review for Final Exam Section VII. Proportions and Percents Comprehensive Practice Lessons 37-42 Lesson 37: Scale and Proportion Skill: Write ratios of sides

More information

CN#5 Objectives 5/11/ I will be able to describe the effect on perimeter and area when one or more dimensions of a figure are changed.

CN#5 Objectives 5/11/ I will be able to describe the effect on perimeter and area when one or more dimensions of a figure are changed. CN#5 Objectives I will be able to describe the effect on perimeter and area when one or more dimensions of a figure are changed. When the dimensions of a figure are changed proportionally, the figure will

More information

Replacement for a Carpenter s Square

Replacement for a Carpenter s Square Lesson.1 Skills Practice Name Date Replacement for a arpenter s Square Inscribed and ircumscribed Triangles and Quadrilaterals Vocabulary nswer each question. 1. How are inscribed polygons and circumscribed

More information

Please mail your completed placement test to the Admissions Office by May 19, 2016.

Please mail your completed placement test to the Admissions Office by May 19, 2016. S T. M ARK S M ATH P LACEMENT Dear new St. Marker, Welcome! In order to find the most appropriate math placement for you, I need you to take the enclosed placement test. This test is meant to be taken

More information

MPM 2DI EXAM REVIEW. Monday, June 19, :30 AM 1:00 PM * A PENCIL, SCIENTIFIC CALCULATOR AND RULER ARE REQUIRED *

MPM 2DI EXAM REVIEW. Monday, June 19, :30 AM 1:00 PM * A PENCIL, SCIENTIFIC CALCULATOR AND RULER ARE REQUIRED * NAME: MPM DI EXAM REVIEW Monday, June 19, 017 11:30 AM 1:00 PM * A PENCIL, SCIENTIFIC CALCULATOR AND RULER ARE REQUIRED * Please Note: Your final mark in this course will be calculated as the better of:

More information

Math 99 Project 1 (60 points) Due Thursday 28 th September

Math 99 Project 1 (60 points) Due Thursday 28 th September Math 99 Project 1 (60 points) Due Thursday 28 th September Students Name: This Project is to help you to review some of the concepts from Math 94 that you will use in this class. These questions need to

More information

GEOMETRY (Common Core)

GEOMETRY (Common Core) GEOMETRY (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY (Common Core) Tuesday, June 2, 2015 1:15 to 4:15 p.m., only Student Name: School Name: The possession

More information

Click one of the buttons below or press the enter key EXIT

Click one of the buttons below or press the enter key EXIT Click one of the buttons below or press the enter key In geometry, two polygons are similar when one is a replica (scale model) of the other. Consider Dr. Evil and Mini Me from Mike Meyers hit movie Austin

More information

NTI Work Day #1 Math. 4. What is the slope of the line that passes through the origin and (-3, -2)? a. 3 2 b. 2 3 c. 0 d. 2 3 e.

NTI Work Day #1 Math. 4. What is the slope of the line that passes through the origin and (-3, -2)? a. 3 2 b. 2 3 c. 0 d. 2 3 e. NTI Work Day #1 Math 1. 2 0 + 2 3 2 2 =? a. 4 b. 6 1 4 c. 7 d. 8 3 4 e. 9 3 4 2. The figure below is a graph of which of the following equations? a. y = -3x + 5 b. y = -2x + 2 c. y = 3 2 x 2 d. y = 2 3

More information

12-1 B = B L E S S O N M A S T E R. Name

12-1 B = B L E S S O N M A S T E R. Name L S S O N M S T R 12-1 Q u e s tio n s o n SP U R Ob je c tiv e s R e p re s e n ta tio n s Objective : Perform and analyze size transformations on fi g u res in th e coordinate p lane. 1. Let Q (-3, 4),

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

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

0615geo. Geometry CCSS Regents Exam In the diagram below, congruent figures 1, 2, and 3 are drawn.

0615geo. Geometry CCSS Regents Exam In the diagram below, congruent figures 1, 2, and 3 are drawn. 0615geo 1 Which object is formed when right triangle RST shown below is rotated around leg RS? 4 In the diagram below, congruent figures 1, 2, and 3 are drawn. 1) a pyramid with a square base 2) an isosceles

More information

Chapter 6. Worked-Out Solutions AB 3.61 AC 5.10 BC = 5

Chapter 6. Worked-Out Solutions AB 3.61 AC 5.10 BC = 5 27. onstruct a line ( DF ) with midpoint P parallel to and twice the length of QR. onstruct a line ( EF ) with midpoint R parallel to and twice the length of QP. onstruct a line ( DE ) with midpoint Q

More information

Pre-Algebra Unit 8 Practice Test: Ratios, Rates, & Proportions Answer Section

Pre-Algebra Unit 8 Practice Test: Ratios, Rates, & Proportions Answer Section Pre-Algebra Unit 8 Practice Test: Ratios, Rates, & Proportions Answer Section MULTIPLE CHOICE 1. ANS: B PTS: 1 DIF: L2 REF: -1 Ratios and Unit Rates STA: CA 7.MG.1.1 CA 7.MG.1.3 CA 7.AF.4.2 TOP: -1 Example

More information

a. 0.7 ft per yd b. 0.2 in per in c. 0.6 yd per yd d. 0.6 ft e. 0.2 yd

a. 0.7 ft per yd b. 0.2 in per in c. 0.6 yd per yd d. 0.6 ft e. 0.2 yd 1. The Bluebird zip line starts 42 feet above the ground and ends 6 feet above the ground. The horizontal distance covered by the zip line is 60 yards. Which of the following is the slope of the Bluebird

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Tuesday, June 19, :15 a.m. to 12:15 p.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Tuesday, June 19, :15 a.m. to 12:15 p.m. GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tuesday, June 19, 2018 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any communications

More information

1. The area of the surface of the Atlantic Ocean is approximately 31,830,000 square miles. How is this area written in scientific notation?

1. The area of the surface of the Atlantic Ocean is approximately 31,830,000 square miles. How is this area written in scientific notation? 1. The area of the surface of the tlantic Ocean is approximately 31,830,000 square miles. How is this area written in scientific notation? 3.183 x 10 4 B 3.183 x 10 5 C 3.183 x 10 6 D 3.183 x 10 7 2. 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

Arizona Western College MAT 105 Mathematics for Applied Sciences Final Exam Review Solutions Spring = = 12 (page 43)

Arizona Western College MAT 105 Mathematics for Applied Sciences Final Exam Review Solutions Spring = = 12 (page 43) Arizona Western College MAT 0 Mathematics for Applied Sciences Final Exam Review Solutions Spring 06 Student NAME You are expected to show your process. That means show how you get from the initial problem

More information

Directions: Solve each problem. Write your answer as a simplified radical!

Directions: Solve each problem. Write your answer as a simplified radical! Directions: Simplify completely! 1) 7 ) 7 10 ) 5 + 6 + 7 4 7 4) 4 11 5) ( ) 6) (6w 8 w ) 7) 0 8 48 75 4 5 8) 7 (10 5 5 ) 9) 4 4 5 8 10) 90m n 11) 1) 5m 8 m 0 0 10 80 r r r 1) 5 18k m 14) 7 km 7km Directions:

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 two radii in Circle E.

Name two radii in Circle E. A C E B D Name two radii in Circle E. Unit 4: Prerequisite Terms A C E B D ECandED Unit 4: Prerequisite Terms A C E B D Name all chords in Circle E. Unit 4: Prerequisite Terms A C E B D AD, CD, AB Unit

More information

Regents Exam Questions A.N.5: Direct Variation

Regents Exam Questions A.N.5: Direct Variation Regents Exam Questions A.N.5: Direct Variation www.jmap.org Name: A.N.5: Direct Variation: Solve algebraic problems from situations that involve fractions, decimals, percents (decrease/increase and discount),

More information

7.1 Ratios and Proportions Notes

7.1 Ratios and Proportions Notes 7.1 Ratios and Proportions Notes Ratio Proportion olve the proportions: 1. 5 = x 75 2. x 5 1 = 4 2. 2x + 1 5x 4 = 5 4. x 11 4 = 5. 4 7 = 2x + 5. = 7 x x + 1 7.1 Ratios and Proportions Notes Write and

More information

Name That Triangle! Classifying Triangles on the Coordinate Plane. LESSON 5.1 Assignment

Name That Triangle! Classifying Triangles on the Coordinate Plane. LESSON 5.1 Assignment LESSON.1 Assignment Name Date Name That Triangle! Classifying Triangles on the Coordinate Plane 1. The grid shown is a map of Stoneville and the locations of several businesses in the town. A line segment

More information

Test 4 also includes review problems from earlier sections so study test reviews 1, 2, and 3 also.

Test 4 also includes review problems from earlier sections so study test reviews 1, 2, and 3 also. MATD 0370 ELEMENTARY ALGEBRA REVIEW FOR TEST 4 (1.1-10.1, not including 8.2) Test 4 also includes review problems from earlier sections so study test reviews 1, 2, and 3 also. 1. Factor completely: a 2

More information

1-2 Measuring and Constructing Segments

1-2 Measuring and Constructing Segments Warm Up Simplify. 1. 7 ( 3) 10 2. 1 ( 13) 12 3. 7 1 8 Solve each equation. 4. 2x + 3 = 9x 11 5. 3x = 4x 5 2 5 6. How many numbers are there between and? Infinitely many Standard U1S2 Use length and midpoint

More information

12.1 Triangle Proportionality Theorem

12.1 Triangle Proportionality Theorem Name lass Date 12.1 Triangle Proportionality Theorem ssential Question: When a line parallel to one side of a triangle intersects the other two sides, how does it divide those sides? Resource Locker xplore

More information

Throughout this chapter you will need: pencil ruler protractor. 7.1 Relationship Between Sides in Rightangled. 13 cm 10.5 cm

Throughout this chapter you will need: pencil ruler protractor. 7.1 Relationship Between Sides in Rightangled. 13 cm 10.5 cm 7. Trigonometry In this chapter you will learn aout: the relationship etween the ratio of the sides in a right-angled triangle solving prolems using the trigonometric ratios finding the lengths of unknown

More information

Math 0240 Final Exam Review Questions 11 ( 9) 6(10 4)

Math 0240 Final Exam Review Questions 11 ( 9) 6(10 4) Math 040 Final Eam Review Questions 11 ( 9) 6(10 4) 1. Simplif: 4 8 3 + 8 ( 7). Simplif: 34 3. Simplif ( 5 7) 3( ) 8 6 4. Simplif: (4 3 ) 9 5. Simplif: 6. Evaluate 4 7 3 3 4 5 when and 3 Write each of

More information

5-1 Practice Form K. Midsegments of Triangles. Identify three pairs of parallel segments in the diagram.

5-1 Practice Form K. Midsegments of Triangles. Identify three pairs of parallel segments in the diagram. 5-1 Practice Form K Midsegments of Triangles Identify three pairs of parallel segments in the diagram. 1. 2. 3. Name the segment that is parallel to the given segment. 4. MN 5. ON 6. AB 7. CB 8. OM 9.

More information

Arizona Western College MAT 105 Mathematics for Applied Sciences Final Exam Review Spring 2016

Arizona Western College MAT 105 Mathematics for Applied Sciences Final Exam Review Spring 2016 Arizona Western College MAT 105 Mathematics for Applied Sciences Final Exam Review Spring 016 Student NAME You are expected to show your process. That means show how you get from the initial problem to

More information

LEAVING CERTIFICATE EXAMINATION, 2001 MATHEMATICS HIGHER LEVEL

LEAVING CERTIFICATE EXAMINATION, 2001 MATHEMATICS HIGHER LEVEL M 30 AN ROINN OIDEACHAIS AGUS EOLAÍOCHTA LEAVING CERTIFICATE EXAMINATION, 001 MATHEMATICS HIGHER LEVEL PAPER (300 marks) MONDAY, 11 JUNE MORNING, 930 to 100 Attempt FIVE questions from Section A and ONE

More information

Analytical Geometry- Common Core

Analytical Geometry- Common Core Analytical Geometry- Common Core 1. A B C is a dilation of triangle ABC by a scale factor of ½. The dilation is centered at the point ( 5, 5). Which statement below is true? A. AB = B C A B BC C. AB =

More information

Given that m A = 50 and m B = 100, what is m Z? A. 15 B. 25 C. 30 D. 50

Given that m A = 50 and m B = 100, what is m Z? A. 15 B. 25 C. 30 D. 50 UNIT : SIMILARITY, CONGRUENCE AND PROOFS ) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of. The dilation is centered at ( 4, ). ) Which transformation results in a figure that is similar

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

GEOMETRY. Similar Triangles

GEOMETRY. Similar Triangles GOMTRY Similar Triangles SIMILR TRINGLS N THIR PROPRTIS efinition Two triangles are said to be similar if: (i) Their corresponding angles are equal, and (ii) Their corresponding sides are proportional.

More information

2nd 9 Weeks Test 2. Rankin County Assessment CCSS Math 8th Grade ID: Sample Item Not Available

2nd 9 Weeks Test 2. Rankin County Assessment CCSS Math 8th Grade ID: Sample Item Not Available Rankin County Assessment CCSS Math 8th Grade ID: 201585 2nd 9 Weeks Test 2 Directions: Read the question. Fill in the bubble next to the corresponding question number on your answer sheet. Sample Question

More information

Collecting Like Terms

Collecting Like Terms MPM1D Unit 2: Algebra Lesson 5 Learning goal: how to simplify algebraic expressions by collecting like terms. Date: Collecting Like Terms WARM-UP Example 1: Simplify each expression using exponent laws.

More information

Remember, you may not use a calculator when you take the assessment test.

Remember, you may not use a calculator when you take the assessment test. Elementary Algebra problems you can use for practice. Remember, you may not use a calculator when you take the assessment test. Use these problems to help you get up to speed. Perform the indicated operation.

More information

REVIEW PACKET January 2012

REVIEW PACKET January 2012 NME: REVIEW PKET January 2012 My PERIOD DTE of my EXM TIME of my EXM **THERE RE 10 PROBLEMS IN THIS REVIEW PKET THT RE IDENTIL TO 10 OF THE PROBLEMS ON THE MIDTERM EXM!!!** Your exam is on hapters 1 6

More information

Instructor: Richard Getso Course: Math 200.P10 TR 1:00 PM Spring 2016 (Getso)

Instructor: Richard Getso Course: Math 200.P10 TR 1:00 PM Spring 2016 (Getso) 1/8/016 Practice Test 1 (Chapter 11) Richard Getso Student: Richard Getso Date: 1/8/16 Instructor: Richard Getso Course: Math 00.P10 TR 1:00 PM Spring 016 (Getso) Assignment: Practice Test 1 (Chapter 11)

More information

Geometry Final Exam Review

Geometry Final Exam Review Name: Period: Geometry Final Eam Review 1. Find the volume and surface area of the following figures. a) 5' b) c) Square base, all edges of the pyramid have length of ", h = 5.66". 1' 5 9 16. Find the

More information

Chapter Test. Solve the equation. Check your solution, if possible y = n 13 = 1.4n (8d 5) + 13 = 12d 2 6.

Chapter Test. Solve the equation. Check your solution, if possible y = n 13 = 1.4n (8d 5) + 13 = 12d 2 6. Solve the equation. Check your solution, if possible.. + y =.5. x = 8 3. z 3 = 8. 3.8n 3 =.n + 5 5. (8d 5) + 3 = d 6. j 8 = 8 + j 7..5(p + 5) = 5p +.5 8. 3 t + 8 = 3 (t + 8). (r + 8) = (r + ) 7 Find the

More information

Review for the Final Exam MAT 0024 College Prep Algebra Class

Review for the Final Exam MAT 0024 College Prep Algebra Class Review for the Final Eam Name MAT 00 College Prep Algebra Class Chapter 1 1) Simplify: 6 ( ) + ( ) 1 1 11 ) Simplify: 8 + ( ) ) Simplify: 7 + ( 1) 16 17 10 ) Simplify: () + 1 ) Simplify: + + ( ) ( ) 1

More information

Chapter 8 Similar Triangles

Chapter 8 Similar Triangles Chapter 8 Similar Triangles Key Concepts:.A polygon in which all sides and angles are equal is called a regular polygon.. Properties of similar Triangles: a) Corresponding sides are in the same ratio b)

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Practice Test 1-0308- Chapter 8 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Tell whether the angle is acute, right, obtuse, or straight. 1) 1)

More information

CK-12 Geometry: Similarity by AA

CK-12 Geometry: Similarity by AA CK-12 Geometry: Similarity by AA Learning Objectives Determine whether triangles are similar. Understand AA for similar triangles. Solve problems involving similar triangles. Review Queue a. a. Find the

More information

2. Definition of isosceles triangle 5. 5.

2. Definition of isosceles triangle 5. 5. HSPE Practice Test A Geometry Name Per Teacher Please complete the following problems neatly on your own paper. Show all your work and circle your answers. Transfer your answers for each question to the

More information

Algebra 1 Chapter 1 Test Review

Algebra 1 Chapter 1 Test Review Algebra 1 Chapter 1 Test Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which expression shows 3 less than x? A. B. 3x C. D. 6. Which is a correct

More information

Solutions to Intermediate and College Algebra by Rhodes

Solutions to Intermediate and College Algebra by Rhodes Solutions to Intermediate and College Algebra by Rhodes Section 1.1 1. 20 2. -21 3. 105 4. -5 5. 18 6. -3 7. 65/2 = 32.5 8. -36 9. 539 208 2.591 10. 13/3 11. 81 12. 60 = 2 15 7.746 13. -2 14. -1/3 15.

More information

Measuring Distant Objects

Measuring Distant Objects Measuring Distant Objects 17 March 2014 Measuring Distant Objects 17 March 2014 1/30 How can you measure the length of an object? Ideally, you use a ruler, a tape measure, or some other measuring device.

More information

Multiplication and Division

Multiplication and Division UNIT 3 Multiplication and Division Skaters work as a pair to put on quite a show. Multiplication and division work as a pair to solve many types of problems. 82 UNIT 3 MULTIPLICATION AND DIVISION Isaac

More information

For Your Notebook E XAMPLE 1. Factor when b and c are positive KEY CONCEPT. CHECK (x 1 9)(x 1 2) 5 x 2 1 2x 1 9x Factoring x 2 1 bx 1 c

For Your Notebook E XAMPLE 1. Factor when b and c are positive KEY CONCEPT. CHECK (x 1 9)(x 1 2) 5 x 2 1 2x 1 9x Factoring x 2 1 bx 1 c 9.5 Factor x2 1 bx 1 c Before You factored out the greatest common monomial factor. Now You will factor trinomials of the form x 2 1 bx 1 c. Why So you can find the dimensions of figures, as in Ex. 61.

More information

Math 0240 Final Exam Review Questions 11 ( 9) 6(10 4)

Math 0240 Final Exam Review Questions 11 ( 9) 6(10 4) 11 ( 9) 6(10 4) 1. Simplif: 4 8 3 + 8 ( 7). Simplif: 34 3. Simplif ( 5 7) 3( ) 8 6 4. Simplif: (4 3 ) 9 5. Simplif: 4 7 3 6. Evaluate 3 4 5 when and 3 Write each of the values below in decimal or standard

More information

ACT Review #5 Int Math 3

ACT Review #5 Int Math 3 ACT Review #5 Int Math 3 2. In the figure below, lines j and k are parallel, transversals m and n intersect to form an angle of measure x, and two other angle measures are as marked. What is the value

More information

Identify Ratios, Rates, and Proportions

Identify Ratios, Rates, and Proportions Math 35 "Fall 08" 6.9 "Proportion and Variation" Objectives: * Identify ratios, rates, and proportions * Solve proportions * Use proportions to solve problems * Solve problems involving - Similar triangles

More information

In the same way that you used proportional reasoning to find the length of an arc, you can use proportional reasoning to find the area of a sector.

In the same way that you used proportional reasoning to find the length of an arc, you can use proportional reasoning to find the area of a sector. Name Class Date 16.3 Sector rea Essential Question: How do you find the area of a sector of a circle? Explore Derive the Formula for the rea of a Sector sector of a circle is a region bounded by two radii

More information

Wahkiakum School District, Pre-EOC Geometry 2012

Wahkiakum School District, Pre-EOC Geometry 2012 Pre-EOC Assesment Geometry #1 Wahkiakum School District GEOM Page 1 1. What is the converse of If there are clouds in the sky, then it is raining? 2-2 A If it is raining, then there are clouds in the sky.

More information

Similar Figures & Scale Drawings

Similar Figures & Scale Drawings Similar Figures & Scale Drawings Task Cards 1 10 m 2 3 8 m 4 m The shapes are similar: What is the measure of side HG? What scale factor was used to enlarge Δ UVW to Δ KLM? The two kites are similar. What

More information

2. If an object travels at five feet per second, how many feet does it travel in one hour?

2. If an object travels at five feet per second, how many feet does it travel in one hour? 1. Of the following, which is greater than ½? A. 2/5 B. 4/7 C. 4/9 D. 5/11 E. 6/13 2. If an object travels at five feet per second, how many feet does it travel in one hour? A. 30 B. 300 C. 720 D. 1800

More information

2. Definition of isosceles triangle 5. 5.

2. Definition of isosceles triangle 5. 5. CCS Geometry Assessment Test A Name Per Do this test carefully showing all of your work and, in the case of multiple choice items, filling in the circle of the letter of the correct response. Note which

More information

Use the grid for Use the ordered pairs shown in the table below. x y Which equation represents the data in the table?

Use the grid for Use the ordered pairs shown in the table below. x y Which equation represents the data in the table? Unit Homework Due the day of your test! Use the grid for.. Which point is located at ( 2, )? A point S point F C point G D point H 2. What are the coordinates of point S? A ( 2, 2) C (2, 0) (2, 2) D (2,

More information

Geometry Unit 1 Practice

Geometry Unit 1 Practice Lesson 1-1 1. Persevere in solving problems. Identify each figure. hen give all possible names for the figure. a. S Geometry Unit 1 Practice e. P S G Q. What is a correct name for this plane? W R Z X b..

More information

9-7. a: Solutions vary. Possible solution shown at right. b: Answers vary. Assuming there are no hidden cubes, V = 11 units 3.

9-7. a: Solutions vary. Possible solution shown at right. b: Answers vary. Assuming there are no hidden cubes, V = 11 units 3. Lesson 9.1.1 9-7. a: Solutions vary. Possible solution shown at right. b: Answers vary. Assuming there are no hidden cubes, V = 11 units 0 0 1 1 1 1 9-8. a: 4 5 b: 196:1 c: 9:1 9-9. Since the perimeter

More information

WOCOMAL. Varsity Meet #1. October 9, 2002

WOCOMAL. Varsity Meet #1. October 9, 2002 WOCOMAL Varsity Meet #1 October 9, 2002 October 9, 2002 Varsity Meet#1 ROUND#1: Arithmetic - No Calculators Allowed 1. The formula W = 5.5( d + 8) gives the normal weight W in pounds of a person who is

More information

Year 9 Term 3 Homework

Year 9 Term 3 Homework Yimin Math Centre Year 9 Term 3 Homework Student Name: Grade: Date: Score: Table of contents 5 Year 9 Term 3 Week 5 Homework 1 5.1 Geometry (Review)................................... 1 5.1.1 Angle sum

More information

NAME: Date: HOMEWORK: C1. Question Obtained. Total/100 A 80 B 70 C 60 D 50 E 40 U 39

NAME: Date: HOMEWORK: C1. Question Obtained. Total/100 A 80 B 70 C 60 D 50 E 40 U 39 NAME: Date: HOMEWORK: C1 Question Obtained 1 2 3 4 5 6 7 8 9 10 Total/100 A 80 B 70 C 60 D 50 E 40 U 39 1. Figure 2 y A(1, 7) B(20, 7) D(8, 2) O x C(p, q) The points A(1, 7), B(20, 7) and C(p, q) form

More information

Adventures in Problem Solving

Adventures in Problem Solving Adventures in Problem Solving Ian VanderBurgh (ian.vanderburgh@uwaterloo.ca) Centre for Education in Mathematics and Computing Faculty of Mathematics, University of Waterloo cemc.uwaterloo.ca Saturday

More information

INTERNATIONAL INDIAN SCHOOL, RIYADH. 11cm. Find the surface area of the cuboid (240cm 2 )

INTERNATIONAL INDIAN SCHOOL, RIYADH. 11cm. Find the surface area of the cuboid (240cm 2 ) INTERNATIONAL INDIAN SCHOOL, RIYADH CLASS: IX SUBJECT: MATHEMATICS 1. SURFACE AREAS AND VOLUMES 1. The diagonal of a cube is 12cm. Find its volume. 2. If the lateral surface area of a cube is 1600cm 2,

More information

5. Simplify completely. (Assume any variable in the denominator is nonzero.)

5. Simplify completely. (Assume any variable in the denominator is nonzero.) MATD 0330 BASIC MATH SKILLS REVIEW FOR TEST (No Calculator Allowe Allowed Materials: Scratch Paper Only Test 1 is comprehensive and covers new material from:.4.6, 3.1 3.4, and 4.1 4.3 1. Write 89 6 as

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

Evaluations with Positive and Negative Numbers (page 631)

Evaluations with Positive and Negative Numbers (page 631) LESSON Name 91 Evaluations with Positive and Negative Numbers (page 631) When evaluating expressions with negative numbers, use parentheses to help prevent making mistakes with signs. Example: Evaluate

More information

Properties of Triangles and Four-Sided Figures Lesson 13.1 Classifying Triangles

Properties of Triangles and Four-Sided Figures Lesson 13.1 Classifying Triangles HPTR13 Properties of Triangles and our-sided igures Lesson 13.1 lassifying Triangles 1. lassify the following triangles by sides as a scalene triangle, an isosceles triangle, or an equilateral triangle.

More information

Summer Review for Mathematical Studies Rising 12 th graders

Summer Review for Mathematical Studies Rising 12 th graders Summer Review for Mathematical Studies Rising 12 th graders Due the first day of school in August 2017. Please show all work and round to 3 significant digits. A graphing calculator is required for these

More information

( ) Chapter 7 ( ) ( ) ( ) ( ) Exercise Set The greatest common factor is x + 3.

( ) Chapter 7 ( ) ( ) ( ) ( ) Exercise Set The greatest common factor is x + 3. Chapter 7 Exercise Set 7.1 1. A prime number is an integer greater than 1 that has exactly two factors, itself and 1. 3. To factor an expression means to write the expression as the product of factors.

More information

Relationships of Side Lengths and Angle Measures. Theorem: Practice: State the longest side of the triangle. Justify your answer.

Relationships of Side Lengths and Angle Measures. Theorem: Practice: State the longest side of the triangle. Justify your answer. 10R Unit 8 Similarity CW 8.1 Relationships of Side Lengths and Angle Measures HW: Worksheet #8.1 (following these notes) Theorem: Practice: 1. State the longest side of the triangle. Justify your answer..

More information

Chapter 02 Test. 1 Solve the proportion. A 60 B 60 C 1.35 D Solve the proportion. A 5.4 B 7.4 C 1959 D 1.625

Chapter 02 Test. 1 Solve the proportion. A 60 B 60 C 1.35 D Solve the proportion. A 5.4 B 7.4 C 1959 D 1.625 Name: ate: 1 Solve the proportion. 60 60 1.35 1.35 2 Solve the proportion. 5.4 7.4 1959 1.625 3 Solve the equation. 8x 5 = 12x + 1 1 opyright 2005-2006 by Pearson Education Page 1 of 7 4 Solve the equation.

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

Page 1 of 11 Name: 1) Which figure always has exactly four lines of reflection that map the figure onto itself? A) rectangle B) square C) regular octagon D) equilateral triangle ee4caab3 - Page 1 2) In

More information

SAT Subject Test Practice Test II: Math Level I Time 60 minutes, 50 Questions

SAT Subject Test Practice Test II: Math Level I Time 60 minutes, 50 Questions SAT Subject Test Practice Test II: Math Level I Time 60 minutes, 50 Questions All questions in the Math Level 1 and Math Level Tests are multiple-choice questions in which you are asked to choose the BEST

More information

B C. You try: What is the definition of an angle bisector?

B C. You try: What is the definition of an angle bisector? US Geometry 1 What is the definition of a midpoint? The midpoint of a line segment is the point that divides the segment into two congruent segments. That is, M is the midpoint of if M is on and M M. 1

More information

Cumulative Unit Assessment: Unit 1 and Unit 2

Cumulative Unit Assessment: Unit 1 and Unit 2 lass Information School ity State Teacher (Mathematics lass) Student Information Grade First Name Last Name ate of irth (month) (day) (year) Male Female Have you attended a Ramp-Up course since the beginning

More information

Complying with Title IX

Complying with Title IX Complying with Title IX Constant of Proportionality 2 Warm Up Washington Middle School collects canned food for a local community food bank. Last year, there were 180 students enrolled at the school and

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE II. Wednesday, June 21, :15 to 4:15 p.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE II. Wednesday, June 21, :15 to 4:15 p.m. The University of the State of New York REGENTS HIGH SHOOL EXMINTION THREE-YER SEQUENE FOR HIGH SHOOL MTHEMTIS OURSE II Wednesday, June, 000 :5 to 4:5 p.m., only Notice... Scientific calculators must be

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS A. Wednesday, August 16, :30 to 11:30 a.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS A. Wednesday, August 16, :30 to 11:30 a.m. MATHEMATICS A The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS A Wednesday, August 6, 2006 8:30 to :30 a.m., only Print Your Name: Print Your School s Name: Print your

More information

5. Using a compass and straightedge, construct a bisector of the angle shown below. [Leave all construction marks.]

5. Using a compass and straightedge, construct a bisector of the angle shown below. [Leave all construction marks.] Name: Regents Review Session Two Date: Common Core Geometry 1. The diagram below shows AB and DE. Which transformation will move AB onto DE such that point D is the image of point A and point E is the

More information