Given. Segment Addition. Substitution Property of Equality. Division. Subtraction Property of Equality

Size: px
Start display at page:

Download "Given. Segment Addition. Substitution Property of Equality. Division. Subtraction Property of Equality"

Transcription

1 Mastery Test Questions (10) 1. Question: What is the missing step in the following proof? <Given, To Prove, and Proof will go in passage / image area> Given: ABC with DE AC. Prove: Proof: Statement Reason 1. DE AC Given 2. CAB EDB, ACB DEB If two lines are cut by a transversal, the corresponding angles are congruent. 3. ABC DBE AA criterion for similarity. 4.?? Corresponding side of similar triangles are proportional. 5. AB = AD + DB CB = CE + EB Segment Addition AD DB CE EB 6. Substitution Property of Equality Division 8. Subtraction Property of Equality Comment [s1]: It should be termed as intersected. Alt 1: Alt 2: Alt 3: Alt 4: AB AC DB DE AB DB CB EB AB CB ** AB AC CB DE

2 2. Question: The figure shows the blueprint for the construction of a section of an upcoming airport. If Route A and Route B shown in the blueprint are parallel, what will be the distance from Route A to Route B on Route C? Alt 1: 433 feet Alt 2: 975 feet** Alt 3: 1050 feet Alt 4: 1477 feet 3. Question: Lyra and Donna are testing the radio sets they built for their science project. Lyra gets on the roof of a building with one of the sets which is 22 meters high while Donna walks away from the building with the other set. When Donna goes beyond 50 meters from the building, the connection breaks. What is the approximate range of the radio sets? Alt 1: 45 meters Alt 2: 50 meters

3 Alt 3: 55 meters** Alt 4: 62 meters 4. Question: What is the third step in the following proof? <Given, To Prove, and Proof will go in passage / image area> Given: ABC with m ABC = 90 Prove: AB 2 + BC 2 = AC 2 Proof: Statement Reason 1. Draw BD AC construction 2. ABC BDC Angles with the same measure are congruent. 3. Reflexive Property of Congruence 4. ABC BDC AA criterion of similarity BC AC Corresponding sides of similar triangles are 5. DC BC proportional. 6. BC 2 = AC DC cross multiplication 7. ABC ADB Angles with the same measure are congruent. 8. Reflexive Property of Congruence 9. ABC ADB AA criterion of similarity AB AC Corresponding sides of similar triangles are 10. AD AB proportional. 11. AB 2 = AC AD Cross Multiplication 12. AB 2 + BC 2 = AC AD + AC DC Addition 13. AB 2 + BC 2 = AC (AD + DC) Distributive Property 14. AB 2 + BC 2 = AC AC Segment Addition 15. AB 2 + BC 2 = AC 2 Multiplication Alt 1: BDC ADB Alt 2: BCA BCD** Alt 3: BAC BAD

4 Alt 4: DBC BAC 5. Question: Which of the figures show DE BC? Alt 1: Alt 2: Alt 3:

5 Alt 4: ** 6. Question: What is the missing step in the following proof? <Given, To Prove, and Proof will go in passage / image area> Given: ABC with Prove: DE AC. Proof:

6 Statement 1. Given 2.???? Reason AD DB CE EB 3. Using Common Denominators 4. AB = AD + DB CB = CE + EB Segment Addition AB CB 5. Substitution Property of Equality 6. ABC DBE Reflexive Property of Congruence 7. ABC DBE Side-Angle-Side Similarity Theorem Corresponding angles of similar triangles are 8. BAC BDE congruent. If the corresponding angles formed by two lines 9. DE AC cut by a transversal are congruent, then the lines are parallel. Comment [s2]: This should be termed as intersected. Alt 1: Statement : DB EB Reason: Corresponding sides of congruent triangles are congruent. Alt 2: Statement: DE DE Reason: Addition Property of Equality Alt 3: Statement: 1 1** Reason: Addition Property of Equality Alt 4: Statement: AD EB CE DB Reason: Cross Multiplication 7. Question: Which of the following is true if AD AE? DB EC

7 Alt 1: Alt 2: Alt 3: DE FG DE BC ** FG BC Alt 4: DE FG BC 8. Question: Which of the following statements will be always true if BD is the altitude for right triangle ABC? Alt 1: ADB BDC Alt 2: ADB ~ BDC ** AB AC Alt 3: BC BD Alt 4: BAC BDC 9. Question: A pillar needs two beams to support its weight. Based on the diagram, at what height should the short beam connect the pillar to ensure that it's parallel to the long beam?

8 25 feet? 6 feet 9 feet Alt 1: 6 feet Alt 2: 10 feet** Alt 3: 12 feet Alt 4: 15 feet 10 Question: A group of boys are setting up a tent for their camp. The tent needs to be 12 feet high and 16 feet wide. What should be the minimum length of the sticks that the boys should use to setup the walls for the tent? Alt 1: 8 feet Alt 2: 13 feet Alt 3: 15 feet** Alt 4: 18 feet Pre-test Questions (4) 1. Question: What is the missing step in the following proof? Given: ABC with DE AC.

9 Prove: Proof: Statement Reason 1. DE AC Given 2.?? If two lines are cut by a transversal, the corresponding angles are congruent. 3. ABC DBE AA criterion for similarity. AB CB Corresponding side of similar triangles are 4. proportional. 5. AB = AD + DB CB = CE + EB Segment Addition AD DB CE EB 6. Substitution Property of Equality Division 8. Subtraction Property of Equality Comment [s3]: Should be termed as intersected. Alt 1: CAB ACB, EDB DEB Alt 2: ADE DBE, CED EBD Alt 3: CAD ACE, ADE CED Alt 4: CAB EDB, ACB DEB** 2. Question: The image shows the cable length for a cable car rail from point A to B and the ground distance between the two points. What will be the cable length from point B to C? Alt 1: 29 feet

10 Alt 2: 48 feet Alt 3: 56 feet** Alt 4: 60 feet 3. Question: What is the second step in the following proof? Given: ABC with m ABC = 90 Prove: AB 2 + BC 2 = AC 2 Proof: Statement Reason 1. Draw BD AC construction 2. Angles with the same measure are congruent. 3. BCA BCD Reflexive Property of Congruence 4. ABC BDC AA criterion of similarity BC AC Corresponding sides of similar triangles are 5. DC BC proportional. 6. BC 2 = AC DC cross multiplication 7. Angles with the same measure are congruent. 8. BAC BAD Reflexive Property of Congruence 9. ABC ABD AA criterion of similarity AB AC Corresponding sides of similar triangles are 10. AD AB proportional. 11. AB 2 = AC AD Cross Multiplication 12. AB 2 + BC 2 = AC AD + AC DC Addition 13. AB 2 + BC 2 = AC (AD + DC) Distributive Property 14. AB 2 + BC 2 = AC AC Segment Addition 15. AB 2 + BC 2 = AC 2 Multiplication Comment [s4]: It should be written as ADB. Alt 1: ABC BDC** Alt 2: ADB BDC Alt 3: ABC ADB

11 Alt 4: DBC BAC 4. Question: Which of the following ratios are true if FG BC in this figure? AD AE Alt 1: DF EG DF EG Alt 2: FB GC AD AE Alt 3: DB EC AF AG Alt 4: ** FB GC Unit Post-test Questions (4) 1. Question: What is the missing step in the following proof? Given: ABC with. Prove: DE AC

12 Proof: Statement Reason 1. Given Addition Property of Equality AD DB CE EB 3. Using Common Denominators 4. AB = AD + DB CB = CE + EB Segment Addition AB CB 5. Substitution Property of Equality 6.?? Reflexive Property of Congruence 7. ABC DBE Side-Angle-Side Similarity Theorem Corresponding angles of similar triangles are 8. BAC BDE congruent. If the corresponding angles formed by two lines 9. DE AC cut by a transversal are congruent, then the lines are parallel. Comment [s5]: Should be termed as intersected. Alt 1: ABC DBE** Alt 2: BAC BDE Alt 3: ACB DEB Alt 4: BDE ADE Alt 5: CAB DAC 2. Question: A small plane takes off from point A and continues to climb upward in a straight line. The image shows its exact distance from and the ground distance from point A at different points during the take off. What will be its distance from the takeoff point when it's at point C??? B 56 feet A 52 feet 65 feet Alt 1: 70 feet Alt 2: 76 feet

13 Alt 3: 101 feet Alt 4: 126 feet** Alt 5: 134 feet 3. Question: Given a right triangle ABC, what construction do you need to perform while proving the Pythagoras theorem? Alt 1: Alt 2: Alt 3: **

14 Alt 4: Alt 5: 4. Question: Which of the following ratios are true if ADE ABC?

15 AD AE Alt 1: ** DB EC AF AG Alt 2: FB GC AD AE Alt 3: DF EG DF EG Alt 4: FB GC AD AE Alt 5: FB GC End-of-Semester Test Questions (2) 1. Question: What is the missing step in the following proof? Given: ABC with. Prove: DE AC Proof: Statement 1. Given Reason

16 Addition Property of Equality AD DB CE EB 3. Using Common Denominators 4. AB = AD + DB CB = CE + EB Segment Addition AB CB 5. Substitution Property of Equality 6. ABC DBE Reflexive Property of Congruence 7. ABC DBE Side-Angle-Side Similarity Theorem Corresponding angles of similar triangles are 8.?? congruent. If the corresponding angles formed by two lines 9. DE AC cut by a transversal are congruent, then the lines are parallel. Comment [s6]: Should be termed as intersected. Alt 1: BAC ACB Alt 2: BDE DEB Alt 3: ADE DEC Alt 4: BAC BDE** Alt 5: ABC DBE 2. Question: A flight of stairs is supported by two pillars as shown. What is the distance of the second pillar from the bottom of the stairs? 12 feet 6 feet Alt 1: 6 feet Alt 2: 8 feet Alt 3: 12 feet** 4 feet??

17 Alt 4: 16 feet Alt 5: 20 feet

Answer Key. 9.1 Parts of Circles. Chapter 9 Circles. CK-12 Geometry Concepts 1. Answers. 1. diameter. 2. secant. 3. chord. 4.

Answer Key. 9.1 Parts of Circles. Chapter 9 Circles. CK-12 Geometry Concepts 1. Answers. 1. diameter. 2. secant. 3. chord. 4. 9.1 Parts of Circles 1. diameter 2. secant 3. chord 4. point of tangency 5. common external tangent 6. common internal tangent 7. the center 8. radius 9. chord 10. The diameter is the longest chord in

More information

Triangles. Example: In the given figure, S and T are points on PQ and PR respectively of PQR such that ST QR. Determine the length of PR.

Triangles. Example: In the given figure, S and T are points on PQ and PR respectively of PQR such that ST QR. Determine the length of PR. Triangles Two geometric figures having the same shape and size are said to be congruent figures. Two geometric figures having the same shape, but not necessarily the same size, are called similar figures.

More information

Math 3 Review Sheet Ch. 3 November 4, 2011

Math 3 Review Sheet Ch. 3 November 4, 2011 Math 3 Review Sheet Ch. 3 November 4, 2011 Review Sheet: Not all the problems need to be completed. However, you should look over all of them as they could be similar to test problems. Easy: 1, 3, 9, 10,

More information

SHW 1-01 Total: 30 marks

SHW 1-01 Total: 30 marks SHW -0 Total: 30 marks 5. 5 PQR 80 (adj. s on st. line) PQR 55 x 55 40 x 85 6. In XYZ, a 90 40 80 a 50 In PXY, b 50 34 84 M+ 7. AB = AD and BC CD AC BD (prop. of isos. ) y 90 BD = ( + ) = AB BD DA x 60

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

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

SOLUTIONS SECTION A [1] = 27(27 15)(27 25)(27 14) = 27(12)(2)(13) = cm. = s(s a)(s b)(s c)

SOLUTIONS SECTION A [1] = 27(27 15)(27 25)(27 14) = 27(12)(2)(13) = cm. = s(s a)(s b)(s c) 1. (A) 1 1 1 11 1 + 6 6 5 30 5 5 5 5 6 = 6 6 SOLUTIONS SECTION A. (B) Let the angles be x and 3x respectively x+3x = 180 o (sum of angles on same side of transversal is 180 o ) x=36 0 So, larger angle=3x

More information

A plane can be names using a capital cursive letter OR using three points, which are not collinear (not on a straight line)

A plane can be names using a capital cursive letter OR using three points, which are not collinear (not on a straight line) Geometry - Semester 1 Final Review Quadrilaterals (Including some corrections of typos in the original packet) 1. Consider the plane in the diagram. Which are proper names for the plane? Mark all that

More information

Mathematics 2260H Geometry I: Euclidean geometry Trent University, Winter 2012 Quiz Solutions

Mathematics 2260H Geometry I: Euclidean geometry Trent University, Winter 2012 Quiz Solutions Mathematics 2260H Geometry I: Euclidean geometry Trent University, Winter 2012 Quiz Solutions Quiz #1. Tuesday, 17 January, 2012. [10 minutes] 1. Given a line segment AB, use (some of) Postulates I V,

More information

Chapter 7. Geometric Inequalities

Chapter 7. Geometric Inequalities 4. Let m S, then 3 2 m R. Since the angles are supplementary: 3 2580 4568 542 Therefore, m S 42 and m R 38. Part IV 5. Statements Reasons. ABC is not scalene.. Assumption. 2. ABC has at least 2. Definition

More information

TRIANGLES CHAPTER 7. (A) Main Concepts and Results. (B) Multiple Choice Questions

TRIANGLES CHAPTER 7. (A) Main Concepts and Results. (B) Multiple Choice Questions CHAPTER 7 TRIANGLES (A) Main Concepts and Results Triangles and their parts, Congruence of triangles, Congruence and correspondence of vertices, Criteria for Congruence of triangles: (i) SAS (ii) ASA (iii)

More information

Lesson 13: Angle Sum of a Triangle

Lesson 13: Angle Sum of a Triangle Lesson 13: Angle Sum of a Triangle Classwork Concept Development 1 + 2 + 3 = 4 + 5 + 6 = 7 + 8 + 9 = 180 Note that the sum of angles 7 and 9 must equal 90 because of the known right angle in the right

More information

Similarity of Triangle

Similarity of Triangle Similarity of Triangle 95 17 Similarity of Triangle 17.1 INTRODUCTION Looking around you will see many objects which are of the same shape but of same or different sizes. For examples, leaves of a tree

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

Geometry 3 SIMILARITY & CONGRUENCY Congruency: When two figures have same shape and size, then they are said to be congruent figure. The phenomena between these two figures is said to be congruency. CONDITIONS

More information

Geometry Problem Solving Drill 08: Congruent Triangles

Geometry Problem Solving Drill 08: Congruent Triangles Geometry Problem Solving Drill 08: Congruent Triangles Question No. 1 of 10 Question 1. The following triangles are congruent. What is the value of x? Question #01 (A) 13.33 (B) 10 (C) 31 (D) 18 You set

More information

Day 6: Triangle Congruence, Correspondence and Styles of Proof

Day 6: Triangle Congruence, Correspondence and Styles of Proof Name: Day 6: Triangle Congruence, Correspondence and Styles of Proof Date: Geometry CC (M1D) Opening Exercise Given: CE bisects BD Statements 1. bisects 1.Given CE BD Reasons 2. 2. Define congruence in

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

THEOREMS WE KNOW PROJECT

THEOREMS WE KNOW PROJECT 1 This is a list of all of the theorems that you know and that will be helpful when working on proofs for the rest of the unit. In the Notes section I would like you to write anything that will help you

More information

Postulates and Theorems in Proofs

Postulates and Theorems in Proofs Postulates and Theorems in Proofs A Postulate is a statement whose truth is accepted without proof A Theorem is a statement that is proved by deductive reasoning. The Reflexive Property of Equality: a

More information

Triangles. 3.In the following fig. AB = AC and BD = DC, then ADC = (A) 60 (B) 120 (C) 90 (D) none 4.In the Fig. given below, find Z.

Triangles. 3.In the following fig. AB = AC and BD = DC, then ADC = (A) 60 (B) 120 (C) 90 (D) none 4.In the Fig. given below, find Z. Triangles 1.Two sides of a triangle are 7 cm and 10 cm. Which of the following length can be the length of the third side? (A) 19 cm. (B) 17 cm. (C) 23 cm. of these. 2.Can 80, 75 and 20 form a triangle?

More information

Geometry - Review for Final Chapters 5 and 6

Geometry - Review for Final Chapters 5 and 6 Class: Date: Geometry - Review for Final Chapters 5 and 6 1. Classify PQR by its sides. Then determine whether it is a right triangle. a. scalene ; right c. scalene ; not right b. isoceles ; not right

More information

Geometry Midterm Exam Review 3. Square BERT is transformed to create the image B E R T, as shown.

Geometry Midterm Exam Review 3. Square BERT is transformed to create the image B E R T, as shown. 1. Reflect FOXY across line y = x. 3. Square BERT is transformed to create the image B E R T, as shown. 2. Parallelogram SHAQ is shown. Point E is the midpoint of segment SH. Point F is the midpoint of

More information

Angles of Elevation and Depression

Angles of Elevation and Depression Angles of Elevation and Depression Study the following figure carefully. angle of elevation angle of depression When we see an object above us, the angle between our line of sight and the horizontal is

More information

1) Exercise 1 In the diagram, ABC = AED, AD = 3, DB = 2 and AE = 2. Determine the length of EC. Solution:

1) Exercise 1 In the diagram, ABC = AED, AD = 3, DB = 2 and AE = 2. Determine the length of EC. Solution: 1) Exercise 1 In the diagram, ABC = AED, AD = 3, DB = 2 and AE = 2. Determine the length of EC. Solution: First, we show that AED and ABC are similar. Since DAE = BAC and ABC = AED, we have that AED is

More information

Maths Module 4: Geometry. Teacher s Guide

Maths Module 4: Geometry. Teacher s Guide Maths Module 4: Geometry Teacher s Guide 1. Shapes 1.1 Angles Maths Module 4 : Geometry and Trigonometry, Teacher s Guide - page 2 Practice - Answers i. a) a = 48 o b) b = 106 o, c = 74 o, d = 74 o c)

More information

Ratios and Proportions

Ratios and Proportions Warm Ups Ratios and Proportions Ratio: expression that compares_ two quantities by division Examples: Proportion: a statement of _equality between two _ratios Examples: Solve examples of proportions with

More information

CONGRUENCE OF TRIANGLES

CONGRUENCE OF TRIANGLES Congruence of Triangles 11 CONGRUENCE OF TRIANGLES You might have observed that leaves of different trees have different shapes, but leaves of the same tree have almost the same shape. Although they may

More information

Honors Geometry Mid-Term Exam Review

Honors Geometry Mid-Term Exam Review Class: Date: Honors Geometry Mid-Term Exam Review Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. Classify the triangle by its sides. The

More information

Fill in the blanks Chapter 10 Circles Exercise 10.1 Question 1: (i) The centre of a circle lies in of the circle. (exterior/ interior) (ii) A point, whose distance from the centre of a circle is greater

More information

Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Ismailia Road Branch

Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Ismailia Road Branch Cairo Governorate Department : Maths Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Sheet Ismailia Road Branch Sheet ( 1) 1-Complete 1. in the parallelogram, each two opposite

More information

RD Sharma Solutions for Class 10 th

RD Sharma Solutions for Class 10 th RD Sharma Solutions for Class 10 th Contents (Click on the Chapter Name to download the solutions for the desired Chapter) Chapter 1 : Real Numbers Chapter 2 : Polynomials Chapter 3 : Pair of Linear Equations

More information

Honors Geometry Review Exercises for the May Exam

Honors Geometry Review Exercises for the May Exam Honors Geometry, Spring Exam Review page 1 Honors Geometry Review Exercises for the May Exam C 1. Given: CA CB < 1 < < 3 < 4 3 4 congruent Prove: CAM CBM Proof: 1 A M B 1. < 1 < 1. given. < 1 is supp to

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

SOLUTIONS TO EXERCISES FOR. MATHEMATICS 133 Part 4. Basic Euclidean concepts and theorems

SOLUTIONS TO EXERCISES FOR. MATHEMATICS 133 Part 4. Basic Euclidean concepts and theorems SOLUTIONS TO EXERCISES FOR MATHEMATICS 133 Part 4 Winter 2009 NOTE ON ILLUSTRATIONS. Drawings for several of the solutions in this file are available in the following file: http://math.ucr.edu/ res/math133/math133solutions04.figures.f13.pdf

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

Higher Order Thinking Skill questions

Higher Order Thinking Skill questions Higher Order Thinking Skill questions TOPIC- Constructions (Class- X) 1. Draw a triangle ABC with sides BC = 6.3cm, AB = 5.2cm and ÐABC = 60. Then construct a triangle whose sides are times the corresponding

More information

Unit 5, Lesson 4.3 Proving the Pythagorean Theorem using Similarity

Unit 5, Lesson 4.3 Proving the Pythagorean Theorem using Similarity Unit 5, Lesson 4.3 Proving the Pythagorean Theorem using Similarity Geometry includes many definitions and statements. Once a statement has been shown to be true, it is called a theorem. Theorems, like

More information

Class IX Chapter 7 Triangles Maths. Exercise 7.1 Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure).

Class IX Chapter 7 Triangles Maths. Exercise 7.1 Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Exercise 7.1 Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD? In ABC and ABD, AC = AD (Given) CAB = DAB (AB bisects

More information

IB MYP Unit 6 Review

IB MYP Unit 6 Review Name: Date: 1. Two triangles are congruent if 1. A. corresponding angles are congruent B. corresponding sides and corresponding angles are congruent C. the angles in each triangle have a sum of 180 D.

More information

Nozha Directorate of Education Form : 2 nd Prep

Nozha Directorate of Education Form : 2 nd Prep Cairo Governorate Department : Maths Nozha Directorate of Education Form : 2 nd Prep Nozha Language Schools Geometry Revision Sheet Ismailia Road Branch Sheet ( 1) 1-Complete 1. In the parallelogram, each

More information

Class IX Chapter 8 Quadrilaterals Maths

Class IX Chapter 8 Quadrilaterals Maths Class IX Chapter 8 Quadrilaterals Maths Exercise 8.1 Question 1: The angles of quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral. Answer: Let the common ratio between

More information

Class IX Chapter 8 Quadrilaterals Maths

Class IX Chapter 8 Quadrilaterals Maths 1 Class IX Chapter 8 Quadrilaterals Maths Exercise 8.1 Question 1: The angles of quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral. Let the common ratio between the angles

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

Lesson 13: Angle Sum of a Triangle

Lesson 13: Angle Sum of a Triangle Student Outcomes Students know the angle sum theorem for triangles; the sum of the interior angles of a triangle is always 180. Students present informal arguments to draw conclusions about the angle sum

More information

Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD?

Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD? Class IX - NCERT Maths Exercise (7.1) Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD? Solution 1: In ABC and ABD,

More information

6 CHAPTER. Triangles. A plane figure bounded by three line segments is called a triangle.

6 CHAPTER. Triangles. A plane figure bounded by three line segments is called a triangle. 6 CHAPTER We are Starting from a Point but want to Make it a Circle of Infinite Radius A plane figure bounded by three line segments is called a triangle We denote a triangle by the symbol In fig ABC has

More information

Class IX Chapter 7 Triangles Maths

Class IX Chapter 7 Triangles Maths Class IX Chapter 7 Triangles Maths 1: Exercise 7.1 Question In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD? In ABC and ABD,

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

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

Aptitude Height and Distance Practice QA - Difficult

Aptitude Height and Distance Practice QA - Difficult Aptitude Height and Distance Practice QA - Difficult 1. A flagstaff is placed on top of a building. The flagstaff and building subtend equal angles at a point on level ground which is 200 m away from the

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

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

8-6. a: 110 b: 70 c: 48 d: a: no b: yes c: no d: yes e: no f: yes g: yes h: no

8-6. a: 110 b: 70 c: 48 d: a: no b: yes c: no d: yes e: no f: yes g: yes h: no Lesson 8.1.1 8-6. a: 110 b: 70 c: 48 d: 108 8-7. a: no b: yes c: no d: yes e: no f: yes g: yes h: no 8-8. b: The measure of an exterior angle of a triangle equals the sum of the measures of its remote

More information

8-6. a: 110 b: 70 c: 48 d: a: no b: yes c: no d: yes e: no f: yes g: yes h: no

8-6. a: 110 b: 70 c: 48 d: a: no b: yes c: no d: yes e: no f: yes g: yes h: no Lesson 8.1.1 8-6. a: 110 b: 70 c: 48 d: 108 8-7. a: no b: yes c: no d: yes e: no f: yes g: yes h: no 8-8. b: The measure of an exterior angle of a triangle equals the sum of the measures of its remote

More information

PLC Papers. Created For:

PLC Papers. Created For: PLC Papers Created For: ed by use of accompanying mark schemes towards the rear to attain 8 out of 10 marks over time by completing Circle Theorems 1 Grade 8 Objective: Apply and prove the standard circle

More information

EXERCISE 10.1 EXERCISE 10.2

EXERCISE 10.1 EXERCISE 10.2 NCERT Class 9 Solved Questions for Chapter: Circle 10 NCERT 10 Class CIRCLES 9 Solved Questions for Chapter: Circle EXERCISE 10.1 Q.1. Fill in the blanks : (i) The centre of a circle lies in of the circle.

More information

0113ge. Geometry Regents Exam In the diagram below, under which transformation is A B C the image of ABC?

0113ge. Geometry Regents Exam In the diagram below, under which transformation is A B C the image of ABC? 0113ge 1 If MNP VWX and PM is the shortest side of MNP, what is the shortest side of VWX? 1) XV ) WX 3) VW 4) NP 4 In the diagram below, under which transformation is A B C the image of ABC? In circle

More information

Basic Quadrilateral Proofs

Basic Quadrilateral Proofs Basic Quadrilateral Proofs For each of the following, draw a diagram with labels, create the givens and proof statement to go with your diagram, then write a two-column proof. Make sure your work is neat

More information

Paper: 03 Class-X-Math: Summative Assessment - I

Paper: 03 Class-X-Math: Summative Assessment - I 1 P a g e Paper: 03 Class-X-Math: Summative Assessment - I Total marks of the paper: 90 Total time of the paper: 3.5 hrs Questions: 1] Triangle ABC is similar to triangle DEF and their areas are 64 cm

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

1. Prove that for every positive integer n there exists an n-digit number divisible by 5 n all of whose digits are odd.

1. Prove that for every positive integer n there exists an n-digit number divisible by 5 n all of whose digits are odd. 32 nd United States of America Mathematical Olympiad Proposed Solutions May, 23 Remark: The general philosophy of this marking scheme follows that of IMO 22. This scheme encourages complete solutions.

More information

Geometry Regents Practice Midterm

Geometry Regents Practice Midterm Class: Date: Geometry Regents Practice Midterm Multiple Choice Identify the choice that best completes the statement or answers the question. 1. ( points) What is the equation of a line that is parallel

More information

BHP BILLITON UNIVERSITY OF MELBOURNE SCHOOL MATHEMATICS COMPETITION, 2003: INTERMEDIATE DIVISION

BHP BILLITON UNIVERSITY OF MELBOURNE SCHOOL MATHEMATICS COMPETITION, 2003: INTERMEDIATE DIVISION BHP BILLITON UNIVERSITY OF MELBOURNE SCHOOL MATHEMATICS COMPETITION, 00: INTERMEDIATE DIVISION 1. A fraction processing machine takes a fraction f and produces a new fraction 1 f. If a fraction f = p is

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

Mathematics 2260H Geometry I: Euclidean geometry Trent University, Fall 2016 Solutions to the Quizzes

Mathematics 2260H Geometry I: Euclidean geometry Trent University, Fall 2016 Solutions to the Quizzes Mathematics 2260H Geometry I: Euclidean geometry Trent University, Fall 2016 Solutions to the Quizzes Quiz #1. Wednesday, 13 September. [10 minutes] 1. Suppose you are given a line (segment) AB. Using

More information

2016 State Mathematics Contest Geometry Test

2016 State Mathematics Contest Geometry Test 2016 State Mathematics Contest Geometry Test In each of the following, choose the BEST answer and record your choice on the answer sheet provided. To ensure correct scoring, be sure to make all erasures

More information

Name Class Date. Additional Vocabulary Support. Reasoning in Algebra and Geometry

Name Class Date. Additional Vocabulary Support. Reasoning in Algebra and Geometry Additional Vocabulary Support Concept List Addition Property of Equality Division Property of Equality Reflexive Property of Equality Subtraction Property of Equality Transitive Property of Equality Distributive

More information

Euclidean Geometry Proofs

Euclidean Geometry Proofs Euclidean Geometry Proofs History Thales (600 BC) First to turn geometry into a logical discipline. Described as the first Greek philosopher and the father of geometry as a deductive study. Relied on rational

More information

Alg. (( Sheet 1 )) [1] Complete : 1) =.. 3) =. 4) 3 a 3 =.. 5) X 3 = 64 then X =. 6) 3 X 6 =... 7) 3

Alg. (( Sheet 1 )) [1] Complete : 1) =.. 3) =. 4) 3 a 3 =.. 5) X 3 = 64 then X =. 6) 3 X 6 =... 7) 3 Cairo Governorate Department : Maths Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Sheet Ismailia Road Branch [1] Complete : 1) 3 216 =.. Alg. (( Sheet 1 )) 1 8 2) 3 ( ) 2 =..

More information

Junior Secondary. A. Errors 1. Absolute error = Estimated value - Exact value

Junior Secondary. A. Errors 1. Absolute error = Estimated value - Exact value Junior Secondary A. Errors. Absolute error = Estimated value - Exact value. Maximum absolute error = Scale interval of the measuring tool 3. Maximum absolute error Absolute error Relative error = or Measured

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

SOLUTION. Taken together, the preceding equations imply that ABC DEF by the SSS criterion for triangle congruence.

SOLUTION. Taken together, the preceding equations imply that ABC DEF by the SSS criterion for triangle congruence. 1. [20 points] Suppose that we have ABC and DEF in the Euclidean plane and points G and H on (BC) and (EF) respectively such that ABG DEH and AGC DHF. Prove that ABC DEF. The first congruence assumption

More information

Grade 7 Lines and Angles

Grade 7 Lines and Angles ID : ww-7-lines-and-angles [1] Grade 7 Lines and Angles For more such worksheets visit www.edugain.com Answer t he quest ions (1) WXYZ is a quadrilateral whose diagonals intersect each other at the point

More information

Grade 7 Lines and Angles

Grade 7 Lines and Angles ID : ae-7-lines-and-angles [1] Grade 7 Lines and Angles For more such worksheets visit www.edugain.com Answer t he quest ions (1) If lines AC and BD intersects at point O such that AOB: BOC = 3:2, f ind

More information

0610ge. Geometry Regents Exam The diagram below shows a right pentagonal prism.

0610ge. Geometry Regents Exam The diagram below shows a right pentagonal prism. 0610ge 1 In the diagram below of circle O, chord AB chord CD, and chord CD chord EF. 3 The diagram below shows a right pentagonal prism. Which statement must be true? 1) CE DF 2) AC DF 3) AC CE 4) EF CD

More information

Grade 7 Triangle and its properties

Grade 7 Triangle and its properties ID : ae-7-triangle-and-its-properties [1] Grade 7 Triangle and its properties For more such worksheets visit www.edugain.com Answer t he quest ions (1) In triangle In ΔABC, D is a point on the side BC

More information

NAME: Mathematics 133, Fall 2013, Examination 3

NAME: Mathematics 133, Fall 2013, Examination 3 NAME: Mathematics 133, Fall 2013, Examination 3 INSTRUCTIONS: Work all questions, and unless indicated otherwise give reasons for your answers. If the problem does not explicitly state that the underlying

More information

Unit 5: Congruency. Part 1 of 3: Intro to Congruency & Proof Pieces. Lessons 5-1 through 5-4

Unit 5: Congruency. Part 1 of 3: Intro to Congruency & Proof Pieces. Lessons 5-1 through 5-4 Name: Geometry Period Unit 5: Congruency Part 1 of 3: Intro to Congruency & Proof Pieces Lessons 5-1 through 5-4 In this unit you must bring the following materials with you to class every day: Please

More information

10. Circles. Q 5 O is the centre of a circle of radius 5 cm. OP AB and OQ CD, AB CD, AB = 6 cm and CD = 8 cm. Determine PQ. Marks (2) Marks (2)

10. Circles. Q 5 O is the centre of a circle of radius 5 cm. OP AB and OQ CD, AB CD, AB = 6 cm and CD = 8 cm. Determine PQ. Marks (2) Marks (2) 10. Circles Q 1 True or False: It is possible to draw two circles passing through three given non-collinear points. Mark (1) Q 2 State the following statement as true or false. Give reasons also.the perpendicular

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

12 Write a two-column proof.

12 Write a two-column proof. Name: Period: Date: ID: A Chapter 4 Review -- GH 1 Find each measure. m 1, m 2, m 3 9 Triangles ABC and AFD are vertical congruent equilateral triangles. Find x and y. 2 Determine whether PQR STU given

More information

Class IX - NCERT Maths Exercise (10.1)

Class IX - NCERT Maths Exercise (10.1) Class IX - NCERT Maths Exercise (10.1) Question 1: Fill in the blanks (i) The centre of a circle lies in of the circle. (exterior/interior) (ii) A point, whose distance from the centre of a circle is greater

More information

Revision Congruency & Similarity Area & Volume of Similar Figures Scales & Maps

Revision Congruency & Similarity Area & Volume of Similar Figures Scales & Maps Question 1: In the quadrilateral ABCD, the diagonals AC and BD intersect at X. AX = BX and DX = CX. AB is parallel to DC. a) Name a pair of congruent triangles. b) Name a pair of similar triangles. a)

More information

9 th CBSE Mega Test - II

9 th CBSE Mega Test - II 9 th CBSE Mega Test - II Time: 3 hours Max. Marks: 90 General Instructions All questions are compulsory. The question paper consists of 34 questions divided into four sections A, B, C and D. Section A

More information

Pythagorean Theorem a= 6.4, b = 12, c = a = 2.1, b = 7.2, c = 7.5

Pythagorean Theorem a= 6.4, b = 12, c = a = 2.1, b = 7.2, c = 7.5 Pythagorean Theorem Do the following lengths form a right triangle? 1. 2. 3. 4. 5. a= 6.4, b = 12, c = 12.2 6. a = 2.1, b = 7.2, c = 7.5 Find each missing length to the nearest tenth. 1. 2. 3. 1 Find the

More information

Properties of the Circle

Properties of the Circle 9 Properties of the Circle TERMINOLOGY Arc: Part of a curve, most commonly a portion of the distance around the circumference of a circle Chord: A straight line joining two points on the circumference

More information

Triangles. Chapter Flowchart. The Chapter Flowcharts give you the gist of the chapter flow in a single glance.

Triangles. Chapter Flowchart. The Chapter Flowcharts give you the gist of the chapter flow in a single glance. Triangles Chapter Flowchart The Chapter Flowcharts give you the gist of the chapter flow in a single glance. Triangle A plane figure bounded by three line segments is called a triangle. Types of Triangles

More information

Foundations of Neutral Geometry

Foundations of Neutral Geometry C H A P T E R 12 Foundations of Neutral Geometry The play is independent of the pages on which it is printed, and pure geometries are independent of lecture rooms, or of any other detail of the physical

More information

CBSE Sample Paper-05 (Solved) SUMMATIVE ASSESSMENT I MATHEMATICS Class IX. Time allowed: 3 hours Maximum Marks: 90. Section A.

CBSE Sample Paper-05 (Solved) SUMMATIVE ASSESSMENT I MATHEMATICS Class IX. Time allowed: 3 hours Maximum Marks: 90. Section A. CBSE Sample Paper-05 (Solved) SUMMATIVE ASSESSMENT I MATHEMATICS Class IX Time allowed: hours Maximum Marks: 90 General Instructions: a) All questions are compulsory. b) The question paper consists of

More information

21. Prove that If one side of the cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle.

21. Prove that If one side of the cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle. 21. Prove that If one side of the cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle. 22. Prove that If two sides of a cyclic quadrilateral are parallel, then

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

Review for Geometry Midterm 2015: Chapters 1-5

Review for Geometry Midterm 2015: Chapters 1-5 Name Period Review for Geometry Midterm 2015: Chapters 1-5 Short Answer 1. What is the length of AC? 2. Tell whether a triangle can have sides with lengths 1, 2, and 3. 3. Danny and Dana start hiking from

More information

SMT 2018 Geometry Test Solutions February 17, 2018

SMT 2018 Geometry Test Solutions February 17, 2018 SMT 018 Geometry Test Solutions February 17, 018 1. Consider a semi-circle with diameter AB. Let points C and D be on diameter AB such that CD forms the base of a square inscribed in the semicircle. Given

More information

CHAPTER 7 TRIANGLES. 7.1 Introduction. 7.2 Congruence of Triangles

CHAPTER 7 TRIANGLES. 7.1 Introduction. 7.2 Congruence of Triangles CHAPTER 7 TRIANGLES 7.1 Introduction You have studied about triangles and their various properties in your earlier classes. You know that a closed figure formed by three intersecting lines is called a

More information

Chapter Start Thinking. 3.1 Warm Up. 1. Sample answer: 3. CG. 5. Sample answer: FE and FG. 6. Sample answer: D. 3.

Chapter Start Thinking. 3.1 Warm Up. 1. Sample answer: 3. CG. 5. Sample answer: FE and FG. 6. Sample answer: D. 3. 7. ( x + )( x 7) 8. ( x )( x + ) 9. ( x 7)( x + ) 0. ( x 5)( x ). ( x )( x ). ( x + )( x 9) Chapter. Start Thinking B. ( x + )( x ). ( x + )( x ) 5. ( x + 5)( x 5) 6. ( x )( x + ) A C 7. ( x 5)( x 7) 8.

More information

Understand and Apply Theorems about Circles

Understand and Apply Theorems about Circles UNIT 4: CIRCLES AND VOLUME This unit investigates the properties of circles and addresses finding the volume of solids. Properties of circles are used to solve problems involving arcs, angles, sectors,

More information

BC Exam Solutions Texas A&M High School Math Contest October 22, 2016

BC Exam Solutions Texas A&M High School Math Contest October 22, 2016 BC Exam Solutions Texas A&M High School Math Contest October, 016 All answers must be simplified, if units are involved, be sure to include them. 1. Given find A + B simplifying as much as possible. 1

More information

Outline. 1 Overview. 2 From Geometry to Numbers. 4 Interlude on Circles. 5 An Area function. 6 Side-splitter. 7 Pythagorean Theorem

Outline. 1 Overview. 2 From Geometry to Numbers. 4 Interlude on Circles. 5 An Area function. 6 Side-splitter. 7 Pythagorean Theorem December 14, 2012 Outline 1 2 3 4 5 6 7 8 Agenda 1 G-SRT4 Context. orems about similarity 2 Proving that there is a field 3 Areas of parallelograms and triangles 4 lunch/discussion: Is it rational to fixate

More information

Visit: ImperialStudy.com For More Study Materials Class IX Chapter 12 Heron s Formula Maths

Visit: ImperialStudy.com For More Study Materials Class IX Chapter 12 Heron s Formula Maths Exercise 1.1 1. Find the area of a triangle whose sides are respectively 150 cm, 10 cm and 00 cm. The triangle whose sides are a = 150 cm b = 10 cm c = 00 cm The area of a triangle = s(s a)(s b)(s c) Here

More information