Notes: Review of Algebra I skills

Size: px
Start display at page:

Download "Notes: Review of Algebra I skills"

Transcription

1 Notes: Review of Algebra I skills Name: Date: Period:

2 Algebra Review: Systems of Equations

3 * If you divide or multiply an inequality by a negative number, then you must reverse the inequality sign!

4 Notes Factoring Trinomials: Process: 1. Draw a by box. a. Place the first term in the upper left-hand box. b. Place the third term in the lower right-hand box.. Determine factors of the product a c that combine (add) to make b and place them in the opposite empty corners. (Use a factor-sum table.) 3. Pull out the GCF from each row. (If b is negative, the larger GCF will be negative.) 4. Reduce the terms inside the boxes as you pull out the GCF. If the reduced terms in each column are the same, then you factored correctly! 5. The pulled out GCF s are one factor, and the reduced terms are the other factor. 6. To solve for x, set each factor = 0, and solve each equation for x. Example 1: Solve by factoring x 7x 18 = 0 x Factors Sum GCF: and reduce List factors Which pair of a c = 18. adds to b = 7? x x x x x x 18 1 and 18 1 and 18 and 9 and = = = = 7 9x x x 18 Example : Solve by factoring 3x 14x = 0 x 7x 18= 0 ( x 9)( x+ ) =0 x 9= 0 and x + = 0 x = 9 and x =

5 Simplifying Radicals When working with the simplification of radicals you must remember some basic information about perfect square numbers. You need to remember: Perfect Squares 4 = x 9 = 3 x 3 16 = 4 x 4 5 = 5 x 5 36 = 6 x 6 49 = 7 x 7 64 = 8 x 8 81 = 9 x = 10 x = 11 x = 1 x = 13 x = 14 x 14 5 = 15 x = 5 x 5 Radicals (square roots) = = 3 = 4 = 5 = 6 = 7 = 8 = 9 = = = = = 14 5 = = 5 While the list of squares and square roots goes on infinitely, the ones appearing in the charts above are the ones most commonly used. To simplify means to find another expression with the same value. It does not mean to find a decimal approximation.

6 To simplify (or reduce) a radical: 1. find the largest perfect square which will divide evenly into the number under your radical sign. This means that when you divide, you get no remainders, no decimals, no fractions. the largest perfect square that Reduce: 48 divides evenly into 48 is 16. If the number under your radical cannot be divided evenly by any of the perfect squares, your radical is already in simplest form and cannot be reduced further.. write the number appearing under your radical as the product (multiplication) of the perfect square and your answer from dividing. 48 = give each number in the product its own radical sign. 48 = 16 3 = reduce the "perfect" radical which you have now created. 48 = 16 3 = 16 3 = 4 5. you now have your answer = What happens if I do not choose the largest perfect square to start the process? If instead of choosing 16 as the largest perfect square to start this process, you choose 4, look what happens = = 4 1 = 4 1 = 1 Unfortunately, this answer is not in simplest form. The 1 can also be divided by a perfect square (4). 1 = 4 3 = 4 3 = 3 = 4 3 If you do not choose the largest perfect square to start the process, you will have to repeat the process. Example: Reduce: 3 50 Don't let the number in front of the radical distract you. It is simply "along for the ride" and will be multiplied times our final answer. The largest perfect square dividing evenly into 50 is = 3 5 = 3 5 Reduce the "perfect" radical and multiply times the 3 (who is "along for the ride") 3 5 = 3 5 = 15

7 Distance Formula, Midpoint & Slope Notes and Practice Pre-AP Geometry Name x = y = Give your answers in simplified radical form! Then also round if necessary. rise Δ y The triangle diagram can also help you find the midpoint and slope! Slope = =. run Δ x Slope of RS = Slope of ST = Midpoint = (average x, average y). To average numbers, ADD them and divide by. Midpoint of RS = Midpoint of ST =

8 Distance Formula, Midpoint & Slope Practice Name: Period: Show your work! For the distance, give your answer in simplified radical form, and also round to the nearest tenth. Draw and label a triangle Find the distance (length) Find the midpoint. Or, if given the Find the slope (write as for the given endpoints. between the endpoints. midpoint, find the missing endpoint. an improper fraction). 1. L(-7, 0), Y(5, 9). B(4, 6), U(1, 3) 3. H(5, 7), K(-9, 3) 4. W(-1, -7), T(-8, -4) 5. A(x 1, y 1 ), B(x, y ) Derive the distance formula. Derive the midpoint formula. Derive the slope formula. 6. D(?,?), F(5, 8). The midpoint is E(4, 3). Find D. 7. D(, 9), F(?,?). The midpoint is E(-1, 6). Find F. 8. D(-3, -8), F(?,?). The midpoint is E(1, -). Find F. 9. The coordinates of the vertices of a quadrilateral are R(-1, 3), S(3, 3), T(5, -1), and U(-, -1). Find the perimeter of the quadrilateral.

9 Algebra Practice with Segment Addition and Midpoint Geometry 1-5 Name: Date: Period: Segment Addition Postulate: If three points A, B, and C are collinear and B is between A and C, then Definition of midpoint: A midpoint is a point that divides a segment into. 1. Use the Segment Addition Postulate to write an equation and solve for x. If AB = 5, find the value of x. Then find AN and NB.. Use the definition of midpoint to write an equation and solve for x. M is the midpoint of RT. Find RM, MT, and RT. #3-6: Find the length of each segment. Tell whether the segments are congruent. 3. AC and BD 4. AD and BE 5. Find the midpoint of AD. 6. Find the midpoint of CD. 7. EG = 100. Find the value of x. Then find EF and FG. 8. Z is the midpoint of XY, and XY = 7. 4(x 5) (x + 15) Draw and label a picture, including congruency marks. Then find XZ. 9. If GJ = 3, find the value of x, GH and HJ. 10. If AX = 45, find the value of y, AQ, QX. 9x 8(x ) 11. Find PD if the coordinate of P is -7 and the coordinate of D is Find SK if the coordinate of S is 17 and the coordinate of K is Find the coordinate of B if AB = 8 and the coordinate of A is Find the coordinate of X if XY = 1 and the coordinate of Y is 0.

10 First, write 1 sentence explaining the relationship between the angles in each problem. (Hints: A linear pair adds to. Supplementary angles add to. Complementary angles add to. Right angles are. Vertical angles are. The sum of adjacent angles the whole. A bisector divides into two parts.) Next, set up an algebraic equation for this relationship. Finally, solve for x or the unknown angle. Show your work! 80 80

11 WS Drawing and Solving Angles and Segments Pre-AP Geometry sections 1-5, 1-6, and 1-7 Name: Date: Period: Draw and label a figure that represents each of these situations. Use congruence marks if possible. Then draw conclusions (if possible) about congruent angles or segments, angle measures, and segment lengths and are linear angles that are also and 4 are complementary but are not congruent. (include both of their measures) adjacent. m 3 = 50. (also include m 4 in your fig.) 19. a b and c b. (there will be 3 lines in this fig.) 0. 5 and 6 are supplementary and also a linear pair. 7 is vertical to 5. m 6 = 150. (include the measures of all 3 angles in your figure) 1. 8 and 9 are vertical angles. m 8 = is adjacent to 9 but m 10 = 0. (include the measures of all 3 angles in your figure). 11 and 1 are a linear pair. 13 is vertical to 11. m 1 = 100. (include all 3 angle measures) 3. d e but e f. (draw all 3 lines in your figure) Line f contains points G and H, and line e is the perpendicular bisector of GH and 15 are not adjacent but they are supplementary. 15 and 16 are adjacent and they are complementary. m 14 = 150. (include all 3 angle measures in your figure. 5. Ray GA bisects RGN. 6. B is the midpoint of AC. 7. Points R, S, and T are collinear (where S is between R and T). RS = 15 and ST = Points X, Y, and Z are collinear (where Y is between X and Z). YZ = 15 and XZ = 40.

12 9. Line p bisects CD at point E. 30. Line MK is the perpendicular bisector of ST. Find m 1 and m for each of the following conditions. Show your work. 31. m 1 is twice m and 3. m 1 is twice m and 1 and are complementary. 1 and are supplementary. 33. m 1 is three less than twice m and 1 and are complementary. 34. m 1 is three less than twice m and 1 and are supplementary. 35. m 1 is six more than five times m and 1 and are a linear pair. 36. m 1 is six more than five times m and 1 and are complementary. Draw a sketch and solve algebraically. Does every arrangement have a solution? 37. Given that AC = 4 and AB = (BC), 38. Given that AC = 18 and AB = 1 5 BC, find AB and BC if: find AB and BC if: a) B is between A and C. AB =, BC = a) B is between A and C. AB =, BC = b) C is between A and B. AB =, BC = b) C is between A and B. AB =, BC = c) A is between B and C. AB =, BC = c) A is between B and C. AB =, BC = 39. D lies in the interior of ABC; m ABC = 10, m ABD = x + 15, m DBC = 3x 5. Does BD bisect ABC? 40. MN bisects KMP; m KMN = 4x 3; m NMP = 3x + 9. Are KMN and NMP complementary angles?

right angle an angle whose measure is exactly 90ᴼ

right angle an angle whose measure is exactly 90ᴼ right angle an angle whose measure is exactly 90ᴼ m B = 90ᴼ B two angles that share a common ray A D C B Vertical Angles A D C B E two angles that are opposite of each other and share a common vertex two

More information

Distance. Warm Ups. Learning Objectives I can find the distance between two points. Football Problem: Bailey. Watson

Distance. Warm Ups. Learning Objectives I can find the distance between two points. Football Problem: Bailey. Watson Distance Warm Ups Learning Objectives I can find the distance between two points. Football Problem: Bailey Watson. Find the distance between the points (, ) and (4, 5). + 4 = c 9 + 6 = c 5 = c 5 = c. Using

More information

Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 1

Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 1 Name: Class: Date: Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 1 Multiple Choice. Identify the choice that best completes the statement or answers the question. 1. Which statement(s)

More information

Writing: Answer each question with complete sentences. 1) Explain what it means to bisect a segment. Why is it impossible to bisect a line?

Writing: Answer each question with complete sentences. 1) Explain what it means to bisect a segment. Why is it impossible to bisect a line? Writing: Answer each question with complete sentences. 1) Explain what it means to bisect a segment. Why is it impossible to bisect a line? 2) Are all linear pairs supplementary angles? Are all supplementary

More information

2) Are all linear pairs supplementary angles? Are all supplementary angles linear pairs? Explain.

2) Are all linear pairs supplementary angles? Are all supplementary angles linear pairs? Explain. 1) Explain what it means to bisect a segment. Why is it impossible to bisect a line? 2) Are all linear pairs supplementary angles? Are all supplementary angles linear pairs? Explain. 3) Explain why a four-legged

More information

Lesson 9.1 Skills Practice

Lesson 9.1 Skills Practice Lesson 9.1 Skills Practice Name Date Earth Measure Introduction to Geometry and Geometric Constructions Vocabulary Write the term that best completes the statement. 1. means to have the same size, shape,

More information

1-2 Measuring and Constructing Segments

1-2 Measuring and Constructing Segments 1-2 Measuring and Constructing Segments Warm Up Lesson Presentation Lesson Quiz Objectives Use length and midpoint of a segment. Construct midpoints and congruent segments. Vocabulary coordinate midpoint

More information

Geometry Midterm REVIEW

Geometry Midterm REVIEW Name: Class: Date: ID: A Geometry Midterm REVIEW Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Given LM = MP and L, M, and P are not collinear. Draw

More information

SM2H Unit 6 Circle Notes

SM2H Unit 6 Circle Notes Name: Period: SM2H Unit 6 Circle Notes 6.1 Circle Vocabulary, Arc and Angle Measures Circle: All points in a plane that are the same distance from a given point, called the center of the circle. Chord:

More information

Name: Date: Period: ID: REVIEW CH 1 TEST REVIEW. 1. Sketch and label an example of each statement. b. A B. a. HG. d. M is the midpoint of PQ. c.

Name: Date: Period: ID: REVIEW CH 1 TEST REVIEW. 1. Sketch and label an example of each statement. b. A B. a. HG. d. M is the midpoint of PQ. c. Name: Date: Period: ID: REVIEW CH 1 TEST REVIEW 1 Sketch and label an example of each statement a HG b A B c ST UV d M is the midpoint of PQ e Angles 1 and 2 are vertical angles f Angle C is a right angle

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

Geometry Chapter 3 3-6: PROVE THEOREMS ABOUT PERPENDICULAR LINES

Geometry Chapter 3 3-6: PROVE THEOREMS ABOUT PERPENDICULAR LINES Geometry Chapter 3 3-6: PROVE THEOREMS ABOUT PERPENDICULAR LINES Warm-Up 1.) What is the distance between the points (2, 3) and (5, 7). 2.) If < 1 and < 2 are complements, and m < 1 = 49, then what is

More information

Triangle Congruence and Similarity Review. Show all work for full credit. 5. In the drawing, what is the measure of angle y?

Triangle Congruence and Similarity Review. Show all work for full credit. 5. In the drawing, what is the measure of angle y? Triangle Congruence and Similarity Review Score Name: Date: Show all work for full credit. 1. In a plane, lines that never meet are called. 5. In the drawing, what is the measure of angle y? A. parallel

More information

Precalculus Summer Assignment 2015

Precalculus Summer Assignment 2015 Precalculus Summer Assignment 2015 The following packet contains topics and definitions that you will be required to know in order to succeed in CP Pre-calculus this year. You are advised to be familiar

More information

Midterm Study Guide Assessment. Question 1. Find the angle measure. (28x + 14) (16x + 62) The measure of the angles are. 11/30/2018 Print Assignment

Midterm Study Guide Assessment. Question 1. Find the angle measure. (28x + 14) (16x + 62) The measure of the angles are. 11/30/2018 Print Assignment Question 1. Find the angle measure. (28x + 14) (16x + 62) The measure of the angles are. https://my.hrw.com/wwtb2/viewer/printall_vs5.html?sf2tt3dnj49xcldd29v4qfjhw0nq0ker6b1uuwkuupca0a5fsymn1tdn7y3prlf19pv779ludnoev4cldd29v4

More information

7.5 Proportionality Relationships

7.5 Proportionality Relationships www.ck12.org Chapter 7. Similarity 7.5 Proportionality Relationships Learning Objectives Identify proportional segments when two sides of a triangle are cut by a segment parallel to the third side. Extend

More information

Properties of Isosceles and Equilateral Triangles

Properties of Isosceles and Equilateral Triangles Properties of Isosceles and Equilateral Triangles In an isosceles triangle, the sides and the angles of the triangle are classified by their position in relation to the triangle s congruent sides. Leg

More information

Geometry Practice Midterm

Geometry Practice Midterm Class: Date: Geometry Practice Midterm 2018-19 1. If Z is the midpoint of RT, what are x, RZ, and RT? A. x = 19, RZ = 38, and RT = 76 C. x = 17, RZ = 76, and RT = 38 B. x = 17, RZ = 38, and RT = 76 D.

More information

MTH 250 Graded Assignment 4

MTH 250 Graded Assignment 4 MTH 250 Graded Assignment 4 Measurement Material from Kay, sections 2.4, 3.2, 2.5, 2.6 Q1: Suppose that in a certain metric geometry* satisfying axioms D1 through D3 [Kay, p78], points A, B, C and D are

More information

Chapter Review #1-3. Choose the best answer.

Chapter Review #1-3. Choose the best answer. Chapter Review #1- Choose the best answer. 1. Which statement is NOT true? A Parallel lines do not intersect. B A segment has exactly two endpoints. C Two planes that do not intersect are always skew.

More information

Honors Geometry Semester Review Packet

Honors Geometry Semester Review Packet Honors Geometry Semester Review Packet 1) Explain what it means to bisect a segment. Why is it impossible to bisect a line? 2) Are all linear pairs supplementary angles? Are all supplementary angles linear

More information

Name: 2015 Midterm Review Period: Date:

Name: 2015 Midterm Review Period: Date: GEOMETRY Name: 2015 Midterm Review Period: Date: To be prepared for your midterm, you will need to PRACTICE PROBLEMS and STUDY TERMS from the following chapters. Use this guide to help you practice. UNIT

More information

What s Next? Example in class: 1, 1, 2, 3, 5, 8,,

What s Next? Example in class: 1, 1, 2, 3, 5, 8,, Name: Period: 2.1 Inductive Reasoning What s Next? Example in class: 1, 1, 2, 3, 5, 8,, What are the next two terms in each sequence? 1) 1, 10, 100, 1000,, 2) 7, 3, -1, -5, -9, -13,, 3) 1, 3, 6, 10, 15,

More information

Geometry Arcs and Chords. Geometry Mr. Austin

Geometry Arcs and Chords. Geometry Mr. Austin 10.2 Arcs and Chords Mr. Austin Objectives/Assignment Use properties of arcs of circles, as applied. Use properties of chords of circles. Assignment: pp. 607-608 #3-47 Reminder Quiz after 10.3 and 10.5

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

Unit 1: Introduction to Proof

Unit 1: Introduction to Proof Unit 1: Introduction to Proof Prove geometric theorems both formally and informally using a variety of methods. G.CO.9 Prove and apply theorems about lines and angles. Theorems include but are not restricted

More information

1-2 Measuring and Constructing Segments

1-2 Measuring and Constructing Segments 1-2 Measuring and Constructing Segments Lesson Presentation Lesson Quiz Objectives Use length and midpoint of a segment. Construct midpoints and congruent segments. Vocabulary coordinate midpoint distance

More information

Geometry - Semester 1 Final Review Quadrilaterals

Geometry - Semester 1 Final Review Quadrilaterals Geometry - Semester 1 Final Review Quadrilaterals 1. Consider the plane in the diagram. Which are proper names for the plane? Mark all that apply. a. Plane L b. Plane ABC c. Plane DBC d. Plane E e. Plane

More information

Parallel and Perpendicular Lines

Parallel and Perpendicular Lines Cumulative Test Choose the best answer. 1. Which statement is NOT true? A Parallel lines do not intersect. B A segment has exactly two endpoints. C Two planes that do not intersect are always skew. D A

More information

2.4 Algebraic and Congruence Properties

2.4 Algebraic and Congruence Properties 2.4 Algebraic and Congruence Properties Learning Objectives Understand basic properties of equality and congruence. Solve equations and justify each step in the solution. Use a 2-column format to prove

More information

0809ge. Geometry Regents Exam Based on the diagram below, which statement is true?

0809ge. Geometry Regents Exam Based on the diagram below, which statement is true? 0809ge 1 Based on the diagram below, which statement is true? 3 In the diagram of ABC below, AB AC. The measure of B is 40. 1) a b ) a c 3) b c 4) d e What is the measure of A? 1) 40 ) 50 3) 70 4) 100

More information

Geometry CP Semester 1 Review Packet. answers_december_2012.pdf

Geometry CP Semester 1 Review Packet.  answers_december_2012.pdf Geometry CP Semester 1 Review Packet Name: *If you lose this packet, you may print off your teacher s webpage. If you can t find it on their webpage, you can find one here: http://www.hfhighschool.org/assets/1/7/sem_1_review_packet

More information

Chapter 2 Segment Measurement and Coordinate Graphing

Chapter 2 Segment Measurement and Coordinate Graphing Geometry Concepts Chapter 2 Segment Measurement and Coordinate Graphing 2.2 Find length segments (1.3) 2.3 Compare lengths of segments (1.3) 2.3 Find midpoints of segments (1.7) 2.5 Calculate coordinates

More information

2.8 Proving angle relationships cont. ink.notebook. September 20, page 84 page cont. page 86. page 85. Standards. Cont.

2.8 Proving angle relationships cont. ink.notebook. September 20, page 84 page cont. page 86. page 85. Standards. Cont. 2.8 Proving angle relationships cont. ink.notebook page 84 page 83 2.8 cont. page 85 page 86 Lesson Objectives Standards Lesson Notes 2.8 Proving Angle Relationships Cont. Press the tabs to view details.

More information

Unit 1 Packet Honors Math 2 1

Unit 1 Packet Honors Math 2 1 Unit 1 Packet Honors Math 2 1 Day 1 Homework Part 1 Graph the image of the figure using the transformation given and write the algebraic rule. translation: < 1, -2 > translation: < 0, 3 > Unit 1 Packet

More information

(b) Follow-up visits: December, May, October, March. (c ) 10, 4, -2, -8,..

(b) Follow-up visits: December, May, October, March. (c ) 10, 4, -2, -8,.. Geometry Honors - Chapter 2 Reasoning and Proof Section 2-1 Inductive Reasoning and Conjecture I can explore inductive and deductive reasoning. I can find counterexamples to disprove conjectures. I can

More information

Proofs Practice Proofs Worksheet #2

Proofs Practice Proofs Worksheet #2 Name: No. Per: Date: Serafino Geometry M T W R F 2C Proofs Practice Proofs Worksheet #2 1. Given: O is the midpoint of MN Prove: OW = ON OM = OW 1. O is the midpoint of seg MN Given 2. Segment NO = Segment

More information

GEOMETRY UNIT 1 WORKBOOK. CHAPTER 2 Reasoning and Proof

GEOMETRY UNIT 1 WORKBOOK. CHAPTER 2 Reasoning and Proof GEOMETRY UNIT 1 WORKBOOK CHAPTER 2 Reasoning and Proof 1 2 Notes 5 : Using postulates and diagrams, make valid conclusions about points, lines, and planes. I) Reminder: Rules that are accepted without

More information

Basic Math. Curriculum (358 topics additional topics)

Basic Math. Curriculum (358 topics additional topics) Basic Math This course covers the topics outlined below and is available for use with integrated, interactive ebooks. You can customize the scope and sequence of this course to meet your curricular needs.

More information

1.4 Midpoints and Bisectors

1.4 Midpoints and Bisectors www.ck12.org Chapter 1. Basics of Geometry 1.4 Midpoints and Bisectors Learning Objectives Identify the midpoint of line segments. Identify the bisector of a line segment. Understand and the Angle Bisector

More information

Lesson. Warm Up deductive 2. D. 3. I will go to the store; Law of Detachment. Lesson Practice 31

Lesson. Warm Up deductive 2. D. 3. I will go to the store; Law of Detachment. Lesson Practice 31 Warm Up 1. deductive 2. D b. a and b intersect 1 and 2 are supplementary 2 and 3 are supplementary 3. I will go to the store; Law of Detachment Lesson Practice a. 1. 1 and 2 are. 2. 1 and 3 are. 3. m 1

More information

Prep for the CSU ELM

Prep for the CSU ELM Prep for the CSU ELM This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular

More information

0811ge. Geometry Regents Exam BC, AT = 5, TB = 7, and AV = 10.

0811ge. Geometry Regents Exam BC, AT = 5, TB = 7, and AV = 10. 0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 2) 8 3) 3 4) 6 2 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation

More information

OBJECTIVES UNIT 1. Lesson 1.0

OBJECTIVES UNIT 1. Lesson 1.0 OBJECTIVES UNIT 1 Lesson 1.0 1. Define "set," "element," "finite set," and "infinite set," "empty set," and "null set" and give two examples of each term. 2. Define "subset," "universal set," and "disjoint

More information

Course Readiness and Skills Review Handbook (Topics 1-10, 17) (240 topics, due. on 09/11/2015) Course Readiness (55 topics)

Course Readiness and Skills Review Handbook (Topics 1-10, 17) (240 topics, due. on 09/11/2015) Course Readiness (55 topics) Course Name: Gr. 8 Fall 2015 Course Code: C6HNH-TEK9E ALEKS Course: Middle School Math Course 3 Instructor: Mr. Fernando Course Dates: Begin: 08/31/2015 End: 06/17/2016 Course Content: 642 Topics (637

More information

Geometry Honors Review for Midterm Exam

Geometry Honors Review for Midterm Exam Geometry Honors Review for Midterm Exam Format of Midterm Exam: Scantron Sheet: Always/Sometimes/Never and Multiple Choice 40 Questions @ 1 point each = 40 pts. Free Response: Show all work and write answers

More information

Segment Measurement, Midpoints, & Congruence

Segment Measurement, Midpoints, & Congruence Lesson 2 Lesson 2, page 1 Glencoe Geometry Chapter 1.4 & 1.5 Segment Measurement, Midpoints, & Congruence Last time, we looked at points, lines, and planes. Today we are going to further investigate lines,

More information

7. m JHI = ( ) and m GHI = ( ) and m JHG = 65. Find m JHI and m GHI.

7. m JHI = ( ) and m GHI = ( ) and m JHG = 65. Find m JHI and m GHI. 1. Name three points in the diagram that are not collinear. 2. If RS = 44 and QS = 68, find QR. 3. R, S, and T are collinear. S is between R and T. RS = 2w + 1, ST = w 1, and RT = 18. Use the Segment Addition

More information

Geometry Summer Review Packet Page 1

Geometry Summer Review Packet Page 1 June 017 Dear Geometry Students and Parents: Welcome to Geometry! For the 017-018 school year, we would like to focus your attention to the fact that many concepts from Algebra I are infused into Geometry.

More information

0114ge. Geometry Regents Exam 0114

0114ge. Geometry Regents Exam 0114 0114ge 1 The midpoint of AB is M(4, 2). If the coordinates of A are (6, 4), what are the coordinates of B? 1) (1, 3) 2) (2, 8) 3) (5, 1) 4) (14, 0) 2 Which diagram shows the construction of a 45 angle?

More information

Geometry: A Complete Course

Geometry: A Complete Course Geometry: omplete ourse (with Trigonometry) Module - Student WorkText Written by: Thomas. lark Larry. ollins RRT 4/2010 6. In the figure below, and share the common segment. Prove the following conditional

More information

HW Set #1: Problems #1-8 For #1-4, choose the best answer for each multiple choice question.

HW Set #1: Problems #1-8 For #1-4, choose the best answer for each multiple choice question. Geometry Homework Worksheets: Chapter 2 HW Set #1: Problems #1-8 For #1-4, choose the best answer for each multiple choice question. 1. Which of the following statements is/are always true? I. adjacent

More information

Chapter 2. Reasoning and Proof

Chapter 2. Reasoning and Proof Chapter 2 Reasoning and Proof 2.1 Use Inductive Reasoning Objective: Describe patterns and use deductive reasoning. Essential Question: How do you use inductive reasoning in mathematics? Common Core: CC.9-12.G.CO.9

More information

These are the skills you should be proficient in performing before you get to Pre-AP Calculus.

These are the skills you should be proficient in performing before you get to Pre-AP Calculus. Fort Zumwalt School District PRE-AP CALCULUS SUMMER REVIEW PACKET Name: 1. This packet is to be handed in to your Pre AP Calculus teacher on the first day of the school year. 2. All work must be shown

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

1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT.

1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. 1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would prove l m? 1) 2.5 2) 4.5 3)

More information

Geometry 1 st Semester review Name

Geometry 1 st Semester review Name Geometry 1 st Semester review Name 1. What are the next three numbers in this sequence? 0, 3, 9, 18, For xercises 2 4, refer to the figure to the right. j k 2. Name the point(s) collinear to points H and

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

Pre Algebra and Introductory Algebra

Pre Algebra and Introductory Algebra Pre Algebra and Introductory Algebra This course covers the topics outlined below and is available for use with integrated, interactive ebooks. You can customize the scope and sequence of this course to

More information

Algebra II Unit #2 4.6 NOTES: Solving Quadratic Equations (More Methods) Block:

Algebra II Unit #2 4.6 NOTES: Solving Quadratic Equations (More Methods) Block: Algebra II Unit # Name: 4.6 NOTES: Solving Quadratic Equations (More Methods) Block: (A) Background Skills - Simplifying Radicals To simplify a radical that is not a perfect square: 50 8 300 7 7 98 (B)

More information

Evaluate the expression if x = 2 and y = 5 6x 2y Original problem Substitute the values given into the expression and multiply

Evaluate the expression if x = 2 and y = 5 6x 2y Original problem Substitute the values given into the expression and multiply Name EVALUATING ALGEBRAIC EXPRESSIONS Objective: To evaluate an algebraic expression Example Evaluate the expression if and y = 5 6x y Original problem 6() ( 5) Substitute the values given into the expression

More information

GEOMETRY CHAPTER 2: Deductive Reasoning

GEOMETRY CHAPTER 2: Deductive Reasoning GEOMETRY CHAPTER 2: Deductive Reasoning NAME Page 1 of 34 Section 2-1: If-Then Statements; Converses Conditional Statement: If hypothesis, then conclusion. hypothesis conclusion converse conditional statement

More information

ACTIVITY 15 Continued Lesson 15-2

ACTIVITY 15 Continued Lesson 15-2 Continued PLAN Pacing: 1 class period Chunking the Lesson Examples A, B Try These A B #1 2 Example C Lesson Practice TEACH Bell-Ringer Activity Read the introduction with students and remind them of the

More information

Pre Algebra. Curriculum (634 topics)

Pre Algebra. Curriculum (634 topics) Pre Algebra This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular needs.

More information

Foundations of High School Math

Foundations of High School Math Foundations of High School Math This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to

More information

0112ge. Geometry Regents Exam Line n intersects lines l and m, forming the angles shown in the diagram below.

0112ge. Geometry Regents Exam Line n intersects lines l and m, forming the angles shown in the diagram below. Geometry Regents Exam 011 011ge 1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would

More information

Postulates, Definitions, and Theorems (Chapter 4)

Postulates, Definitions, and Theorems (Chapter 4) Postulates, Definitions, and Theorems (Chapter 4) Segment Addition Postulate (SAP) All segments AB and BC have unique real number measures AB and BC such that: ABCBC = AC if and only if B is between A

More information

Segment Measurement, Midpoints, & Congruence

Segment Measurement, Midpoints, & Congruence Lesson 2 Lesson 2, page 1 Glencoe Geometry Chapter 1.4 & 1.5 Segment Measurement, Midpoints, & Congruence Last time, we looked at points, lines, and planes. Today we are going to further investigate lines,

More information

Geometry Summer Assignment

Geometry Summer Assignment 2018-2019 Geometry Summer Assignment You must show all work to earn full credit. This assignment will be due Friday, August 24, 2018. It will be worth 50 points. All of these skills are necessary to be

More information

0612ge. Geometry Regents Exam

0612ge. Geometry Regents Exam 0612ge 1 Triangle ABC is graphed on the set of axes below. 3 As shown in the diagram below, EF intersects planes P, Q, and R. Which transformation produces an image that is similar to, but not congruent

More information

4.3. Although geometry is a mathematical study, it has a history that is very much tied. Keep It in Proportion. Theorems About Proportionality

4.3. Although geometry is a mathematical study, it has a history that is very much tied. Keep It in Proportion. Theorems About Proportionality Keep It in Proportion Theorems About Proportionality.3 Learning Goals In this lesson, you will: Prove the Angle Bisector/Proportional Side Theorem. Prove the Triangle Proportionality Theorem. Prove the

More information

UNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS. 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1).

UNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS. 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1). 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1). The dilation is Which statement is true? A. B. C. D. AB B' C' A' B' BC AB BC A' B' B' C' AB BC A' B' D'

More information

Write a 2-column or flow chart proof for the following:

Write a 2-column or flow chart proof for the following: Proofs Study Guide Write a 2-column or flow chart proof for the following: If 6 = a + 2, ten a = 16. 4 Write a 2-column or flow chart proof for the following: If 9x 7 = 7, ten x = 0. Write a 2-column or

More information

Skills Practice Skills Practice for Lesson 9.1

Skills Practice Skills Practice for Lesson 9.1 Skills Practice Skills Practice for Lesson.1 Name Date Meeting Friends The Distance Formula Vocabular Define the term in our own words. 1. Distance Formula Problem Set Archaeologists map the location of

More information

Foundations 5 Curriculum Guide

Foundations 5 Curriculum Guide 1. Review: Natural Numbers...3 2. Reading and Writing Natural Numbers...6 3. Lines, Rays, and Line Segments...8 4. Comparing Natural Numbers... 12 5. Rounding Numbers... 15 6. Adding Natural Numbers...

More information

Midpoint M of points (x1, y1) and (x2, y2) = 1 2

Midpoint M of points (x1, y1) and (x2, y2) = 1 2 Geometry Semester 1 Exam Study Guide Name Date Block Preparing for the Semester Exam Use notes, homework, checkpoints, quizzes, and tests to prepare. If you lost any of the notes, reprint them from my

More information

Math 75 Mini-Mod Due Dates Spring 2016

Math 75 Mini-Mod Due Dates Spring 2016 Mini-Mod 1 Whole Numbers Due: 4/3 1.1 Whole Numbers 1.2 Rounding 1.3 Adding Whole Numbers; Estimation 1.4 Subtracting Whole Numbers 1.5 Basic Problem Solving 1.6 Multiplying Whole Numbers 1.7 Dividing

More information

Test Corrections for Unit 1 Test

Test Corrections for Unit 1 Test MUST READ DIRECTIONS: Read the directions located on www.koltymath.weebly.com to understand how to properly do test corrections. Ask for clarification from your teacher if there are parts that you are

More information

LESSON 6.3 POLYNOMIAL OPERATIONS II

LESSON 6.3 POLYNOMIAL OPERATIONS II LESSON 6.3 POLYNOMIAL OPERATIONS II LESSON 6.3 POLYNOMIALS OPERATIONS II 277 OVERVIEW Here's what you'll learn in this lesson: Multiplying Binomials a. Multiplying binomials by the FOIL method b. Perfect

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

Spring Lake Middle School- Accelerated Math 7 Curriculum Map Updated: January 2018

Spring Lake Middle School- Accelerated Math 7 Curriculum Map Updated: January 2018 Domain Standard Learning Targets Resources Ratios and Proportional Relationships 7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured

More information

Geometry. Unit 2- Reasoning and Proof. Name:

Geometry. Unit 2- Reasoning and Proof. Name: Geometry Unit 2- Reasoning and Proof Name: 1 Geometry Chapter 2 Reasoning and Proof ***In order to get full credit for your assignments they must me done on time and you must SHOW ALL WORK. *** 1. (2-1)

More information

Class : IX(CBSE) Worksheet - 1 Sub : Mathematics Topic : Number system

Class : IX(CBSE) Worksheet - 1 Sub : Mathematics Topic : Number system Class : IX(CBSE) Worksheet - Sub : Mathematics Topic : Number system I. Solve the following:. Insert rational numbers between. Epress 57 65 in the decimal form. 8 and.. Epress. as a fraction in the simplest

More information

Chapter 5: Properties and Attributes of Triangles Review Packet

Chapter 5: Properties and Attributes of Triangles Review Packet Geometry B Name: Date: Block: Chapter 5: Properties and Attributes of Triangles Review Packet All work must be shown to receive full credit. Define the following terms: 1. altitude of a triangle 2. centroid

More information

SUMMATIVE ASSESSMENT I, IX / Class IX

SUMMATIVE ASSESSMENT I, IX / Class IX I, 0 SUMMATIVE ASSESSMENT I, 0 0 MATHEMATICS / MATHEMATICS MATHEMATICS CLASS CLASS - IX - IX IX / Class IX MA-0 90 Time allowed : hours Maximum Marks : 90 (i) (ii) 8 6 0 0 (iii) 8 (iv) (v) General Instructions:

More information

Definitions/Postulates REVIEW!

Definitions/Postulates REVIEW! Do NOW! This is on a worksheet I gave you last week called Practice with Proofs. #1 1) A, B, & C are collinear. B is btwn A & C. AC=32, AB = 2x & BC= 4x+2 2) 1) Given 2) Always start with the givens..

More information

Chapter (Circle) * Circle - circle is locus of such points which are at equidistant from a fixed point in

Chapter (Circle) * Circle - circle is locus of such points which are at equidistant from a fixed point in Chapter - 10 (Circle) Key Concept * Circle - circle is locus of such points which are at equidistant from a fixed point in a plane. * Concentric circle - Circle having same centre called concentric circle.

More information

1. How many planes can be drawn through any three noncollinear points? a. 0 b. 1 c. 2 d. 3. a cm b cm c cm d. 21.

1. How many planes can be drawn through any three noncollinear points? a. 0 b. 1 c. 2 d. 3. a cm b cm c cm d. 21. FALL SEMESTER EXAM REVIEW (Chapters 1-6) CHAPTER 1 1. How many planes can be drawn through any three noncollinear points? a. 0 b. 1 c. 2 d. 3 2. Find the length of PQ. a. 50.9 cm b. 46.3 cm c. 25.7 cm

More information

Geometry S1 (#2211) Foundations in Geometry S1 (#7771)

Geometry S1 (#2211) Foundations in Geometry S1 (#7771) Instructional Materials for WCSD Math Common Finals The Instructional Materials are for student and teacher use and are aligned to the Course Guides for the following courses: Geometry S1 (#2211) Foundations

More information

Geometry/Trig Name: Date: Lesson 1-11 Writing the Equation of a Perpendicular Bisector

Geometry/Trig Name: Date: Lesson 1-11 Writing the Equation of a Perpendicular Bisector Name: Date: Lesson 1-11 Writing the Equation of a Perpendicular Bisector Learning Goals: #14: How do I write the equation of a perpendicular bisector? Warm-up What is the equation of a line that passes

More information

Glossary. Glossary 981. Hawkes Learning Systems. All rights reserved.

Glossary. Glossary 981. Hawkes Learning Systems. All rights reserved. A Glossary Absolute value The distance a number is from 0 on a number line Acute angle An angle whose measure is between 0 and 90 Addends The numbers being added in an addition problem Addition principle

More information

Geometry 21 - More Midterm Practice

Geometry 21 - More Midterm Practice Class: Date: Geometry 21 - More Midterm Practice 1. What are the names of three planes that contain point A? 6. If T is the midpoint of SU, what are ST, TU, and SU? A. ST = 7, TU = 63, and SU = 126 B.

More information

0811ge. Geometry Regents Exam

0811ge. Geometry Regents Exam 0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 ) 8 3) 3 4) 6 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation

More information

Chapter 8: Right Triangles Topic 5: Mean Proportions & Altitude Rules

Chapter 8: Right Triangles Topic 5: Mean Proportions & Altitude Rules Name: Date: Do Now: Use the diagram to complete all parts: a) Find all three angles in each triangle. Chapter 8: Right Triangles Topic 5: Mean Proportions & Altitude Rules b) Find side ZY c) Are these

More information

Unit 10 Geometry Circles. NAME Period

Unit 10 Geometry Circles. NAME Period Unit 10 Geometry Circles NAME Period 1 Geometry Chapter 10 Circles ***In order to get full credit for your assignments they must me done on time and you must SHOW ALL WORK. *** 1. (10-1) Circles and Circumference

More information

Name Geometry Common Core Regents Review Packet - 3. Topic 1 : Equation of a circle

Name Geometry Common Core Regents Review Packet - 3. Topic 1 : Equation of a circle Name Geometry Common Core Regents Review Packet - 3 Topic 1 : Equation of a circle Equation with center (0,0) and radius r Equation with center (h,k) and radius r ( ) ( ) 1. The endpoints of a diameter

More information