Basic Quadrilateral Proofs

Size: px
Start display at page:

Download "Basic Quadrilateral Proofs"

Transcription

1 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 and organized. Quadrilateral Proof: 1. Prove that the sum of the interior angles of a quadrilateral is 360 o. Given: Quadrilateral ABCD Prove: m A + m B + m C + m D = 360 o 1. Quadrilateral ABCD 1. Given 2. m BAC + m B + m BCA = 180 o m CAD + m D + m ACD = 180 o 2. The sum of the interior angles of a triangles add up to 180 o 3. m BAC + m B + m BCA + 3. Addition and Substitution postulates m CAD + m D + m ACD = 360 o 4. m A = m BAC + m CAD 4. Angle addition postulate m C = m BCA + m ACD 5. m A + m B + m C + m D = 360 o 5. Substitution postulate (steps 5,6) Parallelogram Proofs: 2. Prove the opposite sides of a parallelogram are congruent. Prove: AB CD and BC AD 2. AB CD and BC AD 2. Definition of parallelogram 3. BAC DCA and 3. Alternate Interior angles are DAC BCA 4. AC AC 4. Reflexive property of 5. ΔABC ΔCDA 5. ASA 6. AB CD and BC AD 6. CPCTC

2 3. Prove that any pair of consecutive angles of a parallelogram are supplementary. Prove: A and B are supplementary 2. BC AD 2. Definition of parallelogram 3. A and B are supplementary 3. Same side interior angles are supplementary. 4. Prove that opposite angles of a parallelogram are congruent. Prove: A C and B D 2. AB CD and BC AD 2. Definition of parallelogram 3. BAC DCA and DAC 3. Alternate Interior angles are BCA 4. AC AC 4. Reflexive property of 5. ΔABC ΔCDA 5. ASA 6. B D 6. CPCTC 7. A and B are supplementary 7. Property of parallelogram proved in problem #3 C and D are supplementary 8. B D 8. Supplements of angles are (steps 6,7) 5. Prove that the diagonals of a parallelogram bisect each other. Prove: AE CE and BE DE 2. AB CD 2. Definition of parallelogram 3. ABE CDE 3. Alternate Interior Angles are (step 2) BAE DCE 4. AB CD 4. Property of parallelogram proved in #2 5. ΔAEB ΔCED 5. ASA 6. AE CE and BE DE 6. CPCTC

3 Rhombus Proofs: 6. Prove that a rhombus is a parallelogram. Given: Rhombus ABCD Prove: AB CD and BC AD 1. Rhombus ABCD 1. Given 2. AB CD BC AD 2. Definition of rhombus 3. AC AC 3. Reflexive property of 4. ΔABC ΔCDA 4. SSS 5. BAC DCA 5. CPCTC 6. AB CD 6. Converse of alternate-interior angles 7. CAD ACB 7. CPCTC 8. BC AD 8. Converse of alternate-interior angles 7. Prove that the diagonals of a rhombus are perpendicular. Given: Rhombus ABCD Prove: AC BD 1. Rhombus ABCD 1. Given 2. AB BC 2. Definition of rhombus 3. ABCD is a parallelogram 3. Property of a rhombus proved in #6 4. AE CE 4. Property of a parallelogram proved in #5 5. ΔABE ΔCBE 5. SSS 6. AEB CEB 6. CPCTC 7. m AEB = m CEB 7. Definition of segment 8. AEB and CEB are supplementary 8. Two angles that form a linear pair are supplementary 9. m AEB + m CEB = 180 o 9. Definition of supplementary angles 10. m AEB + m AEB = 180 o 10. Substitution postulate (steps 7,9) 11. m AEB = 90 o 11. Division postulate 12. AEB is a right angle 12. Definition of right angle 13. AC BD 13. Definition of perpendicular segments

4 8. Prove that each diagonal of a rhombus bisects a pair of opposite angles. Given: Rhombus ABCD Prove: BAE DAE, BCE DCE, ABE CBE, ADE CDE 1. Rhombus ABCD 1. Given 2. AB CD BC AD 2. Definition of rhombus 3. ABCD is a parallelogram 3. Property of rhombus proved in #6 4. AE CE and BE DE 4. Property of parallelogram proved in #5 5. ΔAEB ΔCEB ΔCED ΔAED 5. SSS 6. BAE DAE, BCE DCE, 6. CPCTC ABE CBE, ADE CDE Rectangles Proofs: 9. Prove that a rectangle is a parallelogram. Given: Rectangle ABCD Prove: AB CD and BC AD 1. Rectangle ABCD 1. Given 2. A B C D 2. Definition of rectangle 3. m A = m B = m C = m D 3. Definition of angles 4. m A + m B + m C + m D = 360 o 4. Property of Quadrilateral proved in # m A = 360 o 5. Substitution postulate (steps 3,7) 6. m A = 90 o 6. Division postulate 7. m B = m C = m D = 90 o 7. Substitution postulate (steps 3,9) 8. m A + m B = 180 o 8. Substitution postulate m A + m D = 180 o 9. A and B are supplementary 9. Definition of supplementary angles A and D are supplementary 10. AB CD and BC AD 10. Converse of same-side interior

5 10. Prove that the diagonals of a rectangle are congruent. Given: Rectangle ABCD Prove: AC BD 1. Rectangle ABCD 1. Given 2. A D 2. Definition of rectangle 3. AD AD 3. Reflexive Property 4. ABCD is parallelogram 4. Property of rectangle proved in #9 5. AB CD 5. Property of parallelogram proved in #2 6. ΔBAD ΔCDA 6. SAS 7. AC BD 7. CPCTC Trapezoid Proofs: 11. Prove each pair of base angles of an isosceles trapezoid is congruent. Given: Isosceles Trapezoid ABCD with BC AD Prove: A D and ABC C 1. Isosceles Trapezoid ABCD with BC AD 1. Given 2. AB CD 2. Definition of Isosceles Trapezoid 3. Construct BE CD 3. Construction 4. Parallelogram EBCD 4. Definition of parallelogram (steps 1,3) 5. BE CD 5. Property of parallelogram proved in #2 6. AB BE 6. Transitive property of (steps 2,5) 7. A AEB 7. Isosceles triangle theorem 8. AEB D 8. Corresponding angles are 9. A D 9. Transitive property 10. A and ABC are supplementary 10. Same side interior angles are supplementary C and D are supplementary 11. ABC C 11. Supplements of angles are (steps 9,10)

6 11. Prove that the diagonals of an isosceles trapezoid are congruent. Given: Isosceles Trapezoid ABCD Prove: AC BD 1. Isosceles Trapezoid ABCD with BC AD 1. Given 2. AB CD 2. Definition of Isosceles Trapezoid 3. BAD CDA 3. Property of Isosceles Trapezoid proved in #11 4. AD AD 4. Reflexive Property 5. ΔBAD ΔCDA 5. SAS 6. AC BD 6. CPCTC Kite Proofs: 12. Prove that the diagonals of a kite are perpendicular. Given: Kite ABCD Prove: AC BD 1. Kite ABCD 1. Given 2. AB BC, AD CD 2. Definition of Kite 3. BAC BCA 3. Isosceles Triangle theorem 4. BD BD 4. Reflexive property of 5. ΔDAB ΔDCB 5. SSS (steps 2,4) 6. ABD CBD 6. CPCTC 7. ΔABE ΔCBE 7. ASA (steps 2,3,6) 8. AEB CEB 8. CPCTC 9. AEB and CEB are supplementary 9. Two angles that form a linear pair are supplementary 10. m AEB + m CEB = 180 o 10. Definition of supplementary 11. m AEB = m CEB 11. Definition of angles (step 8) 12. m AEB + m AEB = 180 o 12. Substitution property (steps 10,11) 13. m AEB = 90 o 13. Division property 14. AC BD 14. Definition of perpendicular segments

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

Rhombi, Rectangles and Squares

Rhombi, Rectangles and Squares Rhombi, Rectangles and Squares Math Practice Return to the Table of Contents 1 Three Special Parallelograms All the same properties of a parallelogram apply to the rhombus, rectangle, and square. Rhombus

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

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

GEO REVIEW TEST #1. 1. In which quadrilateral are the diagonals always congruent?

GEO REVIEW TEST #1. 1. In which quadrilateral are the diagonals always congruent? GEO REVIEW TEST #1 Name: Date: 1. In which quadrilateral are the diagonals always congruent? (1) rectangle (3) rhombus 4. In the accompanying diagram, lines AB and CD intersect at point E. If m AED = (x+10)

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

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 - 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

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

Name: Class: Date: 5. If the diagonals of a rhombus have lengths 6 and 8, then the perimeter of the rhombus is 28. a. True b.

Name: Class: Date: 5. If the diagonals of a rhombus have lengths 6 and 8, then the perimeter of the rhombus is 28. a. True b. Indicate whether the statement is true or false. 1. If the diagonals of a quadrilateral are perpendicular, the quadrilateral must be a square. 2. If M and N are midpoints of sides and of, then. 3. The

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

Grade 9 Lines and Angles

Grade 9 Lines and Angles ID : ww-9-lines-and-angles [1] Grade 9 Lines and Angles For more such worksheets visit www.edugain.com Answer t he quest ions (1) If CD is perpendicular to AB, and CE bisect angle ACB, f ind the angle

More information

Geometry. Midterm Review

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

More information

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

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

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

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

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

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

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

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

Chapter 3 Cumulative Review Answers

Chapter 3 Cumulative Review Answers Chapter 3 Cumulative Review Answers 1a. The triangle inequality is violated. 1b. The sum of the angles is not 180º. 1c. Two angles are equal, but the sides opposite those angles are not equal. 1d. The

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

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

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

More information

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 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

Exercise 10.1 Question 1: Fill in the blanks (i) The centre of a circle lies in of the circle. (exterior/ interior)

Exercise 10.1 Question 1: Fill in the blanks (i) The centre of a circle lies in of the circle. (exterior/ interior) 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 than its radius lies

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

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

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

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

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

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

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

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

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 Note Cards EXAMPLE:

Geometry Note Cards EXAMPLE: Geometry Note Cards EXAMPLE: Lined Side Word and Explanation Blank Side Picture with Statements Sections 12-4 through 12-5 1) Theorem 12-3 (p. 790) 2) Theorem 12-14 (p. 790) 3) Theorem 12-15 (p. 793) 4)

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

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

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

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

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

Geometry AIR Test. Mar 14-3:07 PM. coordinate/algebraic proofs, parallel and perpendicular lines, distance formula, midpoint formula.

Geometry AIR Test. Mar 14-3:07 PM. coordinate/algebraic proofs, parallel and perpendicular lines, distance formula, midpoint formula. Geometry AIR Test Mar 14-3:07 PM Congruence and Proof 33-39% coordinate/algebraic proofs, parallel and perpendicular lines, distance formula, midpoint formula. missing sides on triangles (trig ratios,

More information

Grade 9 Lines and Angles

Grade 9 Lines and Angles ID : sg-9-lines-and-angles [1] Grade 9 Lines and Angles For more such worksheets visit www.edugain.com Answer t he quest ions (1) If AB and PQ are parallel, compute the angle Z. (2) Find the value of a+b.

More information

Class 7 Lines and Angles

Class 7 Lines and Angles ID : in-7-lines-and-angles [1] Class 7 Lines and Angles For more such worksheets visit www.edugain.com Answer the questions (1) ABCD is a quadrilateral whose diagonals intersect each other at point O such

More information

End of Course Review

End of Course Review End of Course Review Geometry AIR Test Mar 14 3:07 PM Test blueprint with important areas: Congruence and Proof 33 39% Transformations, triangles (including ASA, SAS, SSS and CPCTC), proofs, coordinate/algebraic

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

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

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

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

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

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). EOCT Practice Items 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'

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

Geometry Honors: Midterm Exam Review January 2018

Geometry Honors: Midterm Exam Review January 2018 Name: Period: The midterm will cover Chapters 1-6. Geometry Honors: Midterm Exam Review January 2018 You WILL NOT receive a formula sheet, but you need to know the following formulas Make sure you memorize

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

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

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

GCSE: Congruent Triangles Dr J Frost

GCSE: Congruent Triangles Dr J Frost GCSE: Congruent Triangles Dr J Frost (jfrost@tiffin.kingston.sch.uk) www.drfrostmaths.com GCSE Revision Pack Refs: 169, 170 Understand and use SSS, SAS, and conditions to prove the congruence of triangles

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

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

Get your HW and notes out...ready to go!

Get your HW and notes out...ready to go! Get your HW and notes out...ready to go! 1 quadrilateral kite trapezoid parallelogram isos trapezoid rectangle rhombus square What is a Concept map? A Concept map is a diagram that shows relationships

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

+ 10 then give the value

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

More information

Grade 7 Lines and Angles

Grade 7 Lines and Angles ID : ph-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 CD is perpendicular to AB, and CE bisect angle ACB, f ind the angle

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

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

EOC Review MC Questions

EOC Review MC Questions Geometry EOC Review MC Questions Name Date Block You must show all work to receive full credit. - For every 5 answers that are correct, you may receive 5 extra points in the quiz category for a total of

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

0116ge. Geometry Regents Exam RT and SU intersect at O.

0116ge. Geometry Regents Exam RT and SU intersect at O. Geometry Regents Exam 06 06ge What is the equation of a circle with its center at (5, ) and a radius of 3? ) (x 5) + (y + ) = 3 ) (x 5) + (y + ) = 9 3) (x + 5) + (y ) = 3 4) (x + 5) + (y ) = 9 In the diagram

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

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

1. If two angles of a triangle measure 40 and 80, what is the measure of the other angle of the triangle?

1. If two angles of a triangle measure 40 and 80, what is the measure of the other angle of the triangle? 1 For all problems, NOTA stands for None of the Above. 1. If two angles of a triangle measure 40 and 80, what is the measure of the other angle of the triangle? (A) 40 (B) 60 (C) 80 (D) Cannot be determined

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

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

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 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

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

Quads. 4. In the accompanying figure, ABCD is a parallelogram, m A = 2x + 35, and m C = 5x 22. Find the value of x.

Quads. 4. In the accompanying figure, ABCD is a parallelogram, m A = 2x + 35, and m C = 5x 22. Find the value of x. Name: Date: 1. In the accompanying diagram of rhombus ACD, the lengths of the sides A and C are represented by 3x 4 and 2x + 1, respectively. Find the value of x. 4. In the accompanying figure, ACD is

More information

Geometry Problem Solving Drill 13: Parallelograms

Geometry Problem Solving Drill 13: Parallelograms Geometry Problem Solving Drill 13: Parallelograms Question No. 1 of 10 Question 1. Mr. Smith s garden has 4 equal sides. It has 2 pairs of parallel sides. There are no right angles. Choose the most precise

More information

2. In ABC, the measure of angle B is twice the measure of angle A. Angle C measures three times the measure of angle A. If AC = 26, find AB.

2. In ABC, the measure of angle B is twice the measure of angle A. Angle C measures three times the measure of angle A. If AC = 26, find AB. 2009 FGCU Mathematics Competition. Geometry Individual Test 1. You want to prove that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex. Which postulate/theorem

More information

HOLIDAY HOMEWORK - CLASS VIII MATH

HOLIDAY HOMEWORK - CLASS VIII MATH HOLIDAY HOMEWORK - CLASS VIII MATH Assignment I ( Unit: Squares and Square Roots) 1. Which of the following numbers are perfect squares? Justify your answer by prime factorisation method. (a) 1764 (b)

More information

Class 9 Quadrilaterals

Class 9 Quadrilaterals ID : in-9-quadrilaterals [1] Class 9 Quadrilaterals For more such worksheets visit www.edugain.com Answer t he quest ions (1) The diameter of circumcircle of a rectangle is 13 cm and rectangle's width

More information

Higher Geometry Problems

Higher Geometry Problems Higher Geometry Problems (1 Look up Eucidean Geometry on Wikipedia, and write down the English translation given of each of the first four postulates of Euclid. Rewrite each postulate as a clear statement

More information

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

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

More information

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

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

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

9. AD = 7; By the Parallelogram Opposite Sides Theorem (Thm. 7.3), AD = BC. 10. AE = 7; By the Parallelogram Diagonals Theorem (Thm. 7.6), AE = EC.

9. AD = 7; By the Parallelogram Opposite Sides Theorem (Thm. 7.3), AD = BC. 10. AE = 7; By the Parallelogram Diagonals Theorem (Thm. 7.6), AE = EC. 3. Sample answer: Solve 5x = 3x + 1; opposite sides of a parallelogram are congruent; es; You could start b setting the two parts of either diagonal equal to each other b the Parallelogram Diagonals Theorem

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

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

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

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

Higher Geometry Problems

Higher Geometry Problems Higher Geometry Problems (1) Look up Eucidean Geometry on Wikipedia, and write down the English translation given of each of the first four postulates of Euclid. Rewrite each postulate as a clear statement

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

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32 KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 3 SAMPLE PAPER 01 FOR PERIODIC TEST II EXAM (018-19) SUBJECT: MATHEMATICS(041) BLUE PRINT FOR PERIODIC TEST II EXAM: CLASS IX Chapter VSA (1 mark) SA I (

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name: GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, August 17, 2011 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of

More information

Multiple Choice. 3. The polygons are similar, but not necessarily drawn to scale. Find the values of x and y.

Multiple Choice. 3. The polygons are similar, but not necessarily drawn to scale. Find the values of x and y. Accelerated Coordinate Algebra/Analtic Geometr answers the question. Page 1 of 5 Multiple Choice 1. The dashed triangle is an image of the solid triangle. What is the scale factor of the image?. The polgons

More information

Honors Geometry Exam Review January 2015

Honors Geometry Exam Review January 2015 Class: Date: Honors Geometry Exam Review January 2015 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. How many planes can be drawn through any three noncollinear

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