Geometry Problem Solving Drill 07: Properties of Triangles

Size: px
Start display at page:

Download "Geometry Problem Solving Drill 07: Properties of Triangles"

Transcription

1 Geometry Problem Solving Drill 07: Properties of Triangles Question No. 1 of 10 Question 1. In ABC, m A = 44 and m C = 71. Find m B. Question #01 (A) 46 (B) 65 (C) 19 (D) 75 You thought the sum of A and B was 90. B. Correct! You used the Triangle Sum Theorem. You thought the sum of C and B was 90. Using the triangle sum theorem, we have m A + m B + m C = m B + 71 = 180 m B = 65

2 Question No. 2 of 10 Question 2. GHK has a median GS drawn from G to side HK, and R is the centroid. If GS = 36, what is the length of GR? Question #02 (A) 32 (B) 9 (C) 12 (D) 24 When simplifying (2/3)(36), you incorrectly found 36/3 = 16. You used GR = (1/4)(GS). You used GR = (1/3)(GS). D. Correct! You used GR = (2/3)(GS). Using the equivalences for medians and a centroid: GR = (2/3)(36) = 24

3 Question No. 3 of 10 Question 3. In the figure, ABC is an equilateral triangle and AC is a median in ABD. If AB = 24, what is the length of CD? Question #03 (A) 24 (B) 12 (C) 30 (D) 16 A. Correct! You used the definitions of equilateral triangle and median. You thought the length of CD was one-half the length of BC. You found the measure of a base angle in ACD as the length of CD. You divided the sum of AB and BC by 3. All the sides in an equilateral triangle are the same, therefore: AB = AC = BC = 24 On the other hand, BC = CD Therefore, CD = 24

4 Question No. 4 of 10 Question 4. In PQR, the median PT is drawn from P to the side QR, and N is the centroid. If the length of PT is 102, what is the length of NT? Question #04 (A) 32 (B) 36 (C) 34 (D) 52 Check you arithmetic and try again. C. Correct! You used the equivalences for medians and a centroid. You divided 102 by 2 instead of dividing by 3. Using the equivalences for medians and a centroid: NT = (1/3)(PT) = (1/3)(102) = 34

5 Question No. 5 of 10 Question 5. In the right triangle below, m 1 = 59. What is the value of m 1 m 2? Question #05 (A) 31 (B) 28 (C) 38 (D) 48 You found the value of m 2. B. Correct! You first solved for m 2 and then found the difference between the two angles. We are given m 1 = 59 m 1 + m 2 = 90 Solving these equation, we obtain m 2 = 31 Then m 1 m 2 = = 28

6 Question No. 6 of 10 Question 6. In the following isosceles triangle m 1 = 110. What is m 2? Question #06 (A) 70 (B) 30 (C) 55 (D) 35 You found the value of the sum of the base angles. You found the value of half of the vertex angle. D. Correct! You used the Triangle Sum Theorem and the properties of isosceles triangles to find m 2. We have m 2 + m 3 = 180 m 2 = m 3 Therefore, (m 2) = 180 2(m 2) = 70 m 2 = 35

7 Question No. 7 of 10 Question 7. In the isosceles triangle below, m 4 = 124. What is the value of m 1 m 2? Question #07 (A) 12 (B) 14 (C) 6 (D) 68 A. Correct! You used the Exterior Angle Theorem along with the properties of isosceles triangles to solve. m 3 = = 56 Since this is an isosceles triangle: m 3 = m 2 By the Exterior Angle Theorem: m 4 = m 1 + m = m = m 1 Therefore, m 1 m 2 = = 12

8 Question No. 8 of 10 Question 8. In ABC, m A = 90 and m B m C = 20. What is m B? Question #08 (A) 45 (B) 55 (C) 35 (D) 65 B. Correct! You correctly solved the system of equations composed of the given equation along with m B + m C = 90. m B m C = 20 m B + m C = 90 Solve this system of equations to get m B = 55 and m C = 35

9 Question No. 9 of 10 Question 9. Given equilateral ABC and isosceles MNP in which M is 120, which statement is true? Question #09 (A) A = M (B) A = N (C) B = (1/2) N (D) B = 2( N) The measure of an interior angle of an equilateral triangle is not 120. Review the definition of an equilateral triangle and try again. The measure of an interior angle of an equilateral triangle is not 30. Review the definition of an equilateral triangle and try again. You divided N by 2 instead of multiplying by 2. D. Correct! You used the properties of isosceles and equilateral triangles to find the true statement. Since ABC is an equilateral triangle, then A = 60 B = 60 C = 60 We are given M = 120 and P = m Q Using the Triangle Sum Theorem, P = 30 Q = 30 So, B = 2( N) = 2(30) = 60

10 Question No. 10 of 10 Question 10. In ABC, segment CD is an angle bisector and segment AE is an altitude. If m ACB = 38, what is ANC? Question #10 (A) 109 (B) 119 (C) 136 (D) 92 A. Correct! You correctly applied properties of altitude, angle bisector, and the Triangle Sum Theorem. Check your arithmetic in the final step and try again. You forgot to divide m C by 2. While using the Triangle Sum Theorem, you divided m A by 2. In AEC: EAC = = 52 On the other hand, the angle bisector CD gives ACN = 38/2 = 19 Applying the Triangle Sum Theorem to ANC, we conclude ANC = 180 ( ) = 109

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

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

Name: Period: Date: Given: is the bisector of Draw JD and DL such that it makes triangle DJL. Then answer the question. a. 17 b. 73 c. 118 d.

Name: Period: Date: Given: is the bisector of Draw JD and DL such that it makes triangle DJL. Then answer the question. a. 17 b. 73 c. 118 d. Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which statement is not necessarily true? Name: Given: is the bisector of Draw JD and DL such that it makes

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

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

Geometry M1: Unit 3 Practice Exam

Geometry M1: Unit 3 Practice Exam Class: Date: Geometry M1: Unit 3 Practice Exam Short Answer 1. What is the value of x? 2. What is the value of x? 3. What is the value of x? 1 4. Find the value of x. The diagram is not to scale. Given:

More information

0609ge. Geometry Regents Exam AB DE, A D, and B E.

0609ge. Geometry Regents Exam AB DE, A D, and B E. 0609ge 1 Juliann plans on drawing ABC, where the measure of A can range from 50 to 60 and the measure of B can range from 90 to 100. Given these conditions, what is the correct range of measures possible

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

6.2: Isosceles Triangles

6.2: Isosceles Triangles 6.2: Isosceles Triangles Dec 5 4:34 PM 1 Define an Isosceles Triangle. A triangle that has (at least) two sides of equal length. Dec 5 4:34 PM 2 Draw an Isosceles Triangle. Label all parts and mark the

More information

TOPIC 4 Line and Angle Relationships. Good Luck To. DIRECTIONS: Answer each question and show all work in the space provided.

TOPIC 4 Line and Angle Relationships. Good Luck To. DIRECTIONS: Answer each question and show all work in the space provided. Good Luck To Period Date DIRECTIONS: Answer each question and show all work in the space provided. 1. Name a pair of corresponding angles. 1 3 2 4 5 6 7 8 A. 1 and 4 C. 2 and 7 B. 1 and 5 D. 2 and 4 2.

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

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 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

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

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

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

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

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

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

2. If two isosceles triangles have congruent vertex angles, then the triangles must be A. congruent B. right C. equilateral D.

2. If two isosceles triangles have congruent vertex angles, then the triangles must be A. congruent B. right C. equilateral D. 1. If two angles of a triangle measure 56 and 68, the triangle is A. scalene B. isosceles C. obtuse D. right 2. If two isosceles triangles have congruent vertex angles, then the triangles must be A. congruent

More information

The CENTRE for EDUCATION in MATHEMATICS and COMPUTING cemc.uwaterloo.ca Euclid Contest. Wednesday, April 15, 2015

The CENTRE for EDUCATION in MATHEMATICS and COMPUTING cemc.uwaterloo.ca Euclid Contest. Wednesday, April 15, 2015 The CENTRE for EDUCATION in MATHEMATICS and COMPUTING cemc.uwaterloo.ca 015 Euclid Contest Wednesday, April 15, 015 (in North America and South America) Thursday, April 16, 015 (outside of North America

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

Q4. In ABC, AC = AB and B = 50. Find the value of C. SECTION B. Q5. Find two rational numbers between 1 2 and.

Q4. In ABC, AC = AB and B = 50. Find the value of C. SECTION B. Q5. Find two rational numbers between 1 2 and. SUMMATIVE ASSESSMENT 1 (2013 2014) CLASS IX (SET I) SUBJECT : MATHEMATICS Time: 3 hours M.M. : 90 General Instructions : (i) All questions are compulsory. (ii) The question paper consists of 31 questions

More information

USA Mathematics Talent Search

USA Mathematics Talent Search ID#: 036 16 4 1 We begin by noting that a convex regular polygon has interior angle measures (in degrees) that are integers if and only if the exterior angle measures are also integers. Since the sum of

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

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

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

Honors Geometry Term 1 Practice Final

Honors Geometry Term 1 Practice Final Name: Class: Date: ID: A Honors Geometry Term 1 Practice Final Short Answer 1. RT has endpoints R Ê Ë Á 4,2 ˆ, T Ê ËÁ 8, 3 ˆ. Find the coordinates of the midpoint, S, of RT. 5. Line p 1 has equation y

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

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

Indicate the answer choice that best completes the statement or answers the question. Find the volume of the solid.

Indicate the answer choice that best completes the statement or answers the question. Find the volume of the solid. Indicate the answer choice that best completes the statement or answers the question. Find the volume of the solid. A. 252.4 cm 3 B. 126.2 cm 3 C. 492.2 cm 3 D. 703.8 cm 3 F. 576 G. 288 H. 240 I. 336 Powered

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

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

Downloaded from

Downloaded from Triangles 1.In ABC right angled at C, AD is median. Then AB 2 = AC 2 - AD 2 AD 2 - AC 2 3AC 2-4AD 2 (D) 4AD 2-3AC 2 2.Which of the following statement is true? Any two right triangles are similar

More information

Foundation Unit 6 topic test

Foundation Unit 6 topic test Name: Foundation Unit 6 topic test Date: Time: 45 minutes Total marks available: 39 Total marks achieved: Questions Q1. The diagram shows a rectangle, a parallelogram and a triangle. (a) Mark with arrows

More information

Section 7.2: Area of a Triangle

Section 7.2: Area of a Triangle CHAPTER 7 Trigonometric Applications to Triangles Section 7.2: Area of a Triangle Finding Areas Finding Areas Formulas for the Area of a Triangle: 600 University of Houston Department of Mathematics SECTION

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

Q1. The sum of the lengths of any two sides of a triangle is always (greater/lesser) than the length of the third side. askiitians

Q1. The sum of the lengths of any two sides of a triangle is always (greater/lesser) than the length of the third side. askiitians Class: VII Subject: Math s Topic: Properties of triangle No. of Questions: 20 Q1. The sum of the lengths of any two sides of a triangle is always (greater/lesser) than the length of the third side. Greater

More information

10. Show that the conclusion of the. 11. Prove the above Theorem. [Th 6.4.7, p 148] 4. Prove the above Theorem. [Th 6.5.3, p152]

10. Show that the conclusion of the. 11. Prove the above Theorem. [Th 6.4.7, p 148] 4. Prove the above Theorem. [Th 6.5.3, p152] foot of the altitude of ABM from M and let A M 1 B. Prove that then MA > MB if and only if M 1 A > M 1 B. 8. If M is the midpoint of BC then AM is called a median of ABC. Consider ABC such that AB < AC.

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

Eton College King's Scholarship Examination 2013

Eton College King's Scholarship Examination 2013 Eton College King's Scholarship Examination 2013 MATHEMATICS A Answer Question 1 and as many of the other five questions as you can. Question 1 is worth 50 marks. All other questions are worth 10 marks

More information

0110ge. Geometry Regents Exam Which expression best describes the transformation shown in the diagram below?

0110ge. Geometry Regents Exam Which expression best describes the transformation shown in the diagram below? 0110ge 1 In the diagram below of trapezoid RSUT, RS TU, X is the midpoint of RT, and V is the midpoint of SU. 3 Which expression best describes the transformation shown in the diagram below? If RS = 30

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

UNIT-8 SIMILAR TRIANGLES Geometry is the right foundation of all painting, I have decided to teach its rudiments and principles to all youngsters eager for art. 1. ABC is a right-angled triangle, right-angled

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

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

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

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

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

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

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

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

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

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

VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER)

VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER) BY:Prof. RAHUL MISHRA Class :- X QNo. VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER) CIRCLES Subject :- Maths General Instructions Questions M:9999907099,9818932244 1 In the adjoining figures, PQ

More information

1/19 Warm Up Fast answers!

1/19 Warm Up Fast answers! 1/19 Warm Up Fast answers! The altitudes are concurrent at the? Orthocenter The medians are concurrent at the? Centroid The perpendicular bisectors are concurrent at the? Circumcenter The angle bisectors

More information

Circle and Cyclic Quadrilaterals. MARIUS GHERGU School of Mathematics and Statistics University College Dublin

Circle and Cyclic Quadrilaterals. MARIUS GHERGU School of Mathematics and Statistics University College Dublin Circle and Cyclic Quadrilaterals MARIUS GHERGU School of Mathematics and Statistics University College Dublin 3 Basic Facts About Circles A central angle is an angle whose vertex is at the center of the

More information

Chapter - 7. (Triangles) Triangle - A closed figure formed by three intersecting lines is called a triangle. A

Chapter - 7. (Triangles) Triangle - A closed figure formed by three intersecting lines is called a triangle. A Chapter - 7 (Triangles) Triangle - A closed figure formed by three intersecting lines is called a triangle. A triangle has three sides, three angles and three vertices. Congruent figures - Congruent means

More information

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

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

More information

Math 9 Chapter 8 Practice Test

Math 9 Chapter 8 Practice Test Name: Class: Date: ID: A Math 9 Chapter 8 Practice Test Short Answer 1. O is the centre of this circle and point Q is a point of tangency. Determine the value of t. If necessary, give your answer to the

More information

QUESTION BANK ON STRAIGHT LINE AND CIRCLE

QUESTION BANK ON STRAIGHT LINE AND CIRCLE QUESTION BANK ON STRAIGHT LINE AND CIRCLE Select the correct alternative : (Only one is correct) Q. If the lines x + y + = 0 ; 4x + y + 4 = 0 and x + αy + β = 0, where α + β =, are concurrent then α =,

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

LT 2.1 Study Guide and Intervention Classifying Triangles

LT 2.1 Study Guide and Intervention Classifying Triangles LT 2.1 Study Guide and Intervention Classifying Triangles Classify Triangles by Angles One way to classify a triangle is by the measures of its angles. If all three of the angles of a triangle are acute

More information

Vermont Talent Search April 12, 2011 School Year Test 4 Solutions

Vermont Talent Search April 12, 2011 School Year Test 4 Solutions Vermont Talent Search April, 0 School Year 00-0 Test 4 Solutions Problem. Find the area of a triangle whose medians have lengths of 39, 4 and 45. Let M be the center of gravity or centroid of the triangle.

More information

Geometry Chapter 3 & 4 Test

Geometry Chapter 3 & 4 Test Class: Date: Geometry Chapter 3 & 4 Test Use the diagram to find the following. 1. What are three pairs of corresponding angles? A. angles 1 & 2, 3 & 8, and 4 & 7 C. angles 1 & 7, 8 & 6, and 2 & 4 B. angles

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

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

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

Geometry & Measurement Part 3

Geometry & Measurement Part 3 The following worksheets should be used to complete this homework set. Instructions for 1. Complete the problems included in this homework set and enter your answers online. 2. Remember to review the next

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

(D) (A) Q.3 To which of the following circles, the line y x + 3 = 0 is normal at the point ? 2 (A) 2

(D) (A) Q.3 To which of the following circles, the line y x + 3 = 0 is normal at the point ? 2 (A) 2 CIRCLE [STRAIGHT OBJECTIVE TYPE] Q. The line x y + = 0 is tangent to the circle at the point (, 5) and the centre of the circles lies on x y = 4. The radius of the circle is (A) 3 5 (B) 5 3 (C) 5 (D) 5

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

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

Basic Trigonometry. Trigonometry deals with the relations between the sides and angles of triangles.

Basic Trigonometry. Trigonometry deals with the relations between the sides and angles of triangles. Basic Trigonometry Trigonometry deals with the relations between the sides and angles of triangles. A triangle has three sides and three angles. Depending on the size of the angles, triangles can be: -

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

Not all triangles are drawn to scale. 3. Find the missing angles. Then, classify each triangle by it s angles.

Not all triangles are drawn to scale. 3. Find the missing angles. Then, classify each triangle by it s angles. Geometry Name: Date: Chapter 4 Practice Test Block: 1 2 3 4 5 6 7 8 Not all triangles are drawn to scale. 1. The given triangle would be classified as. A] Scalene B] Isosceles C] Equilateral D] none 20

More information

1. In a triangle ABC altitude from C to AB is CF= 8 units and AB has length 6 units. If M and P are midpoints of AF and BC. Find the length of PM.

1. In a triangle ABC altitude from C to AB is CF= 8 units and AB has length 6 units. If M and P are midpoints of AF and BC. Find the length of PM. 1. In a triangle ABC altitude from C to AB is CF= 8 units and AB has length 6 units. If M and P are midpoints of AF and BC. Find the length of PM. 2. Let ABCD be a cyclic quadrilateral inscribed in a circle

More information

Minnesota State High School Mathematics League

Minnesota State High School Mathematics League 01-1 Meet, Individual Event A Question #1 is intended to be a quickie and is worth 1 point. Each of the next three questions is worth points. Place your answer to each question on the line provided. You

More information

SOLUTIONS SECTION A SECTION B

SOLUTIONS SECTION A SECTION B SOLUTIONS SECTION A 1. C (1). A (1) 3. B (1) 4. B (1) 5. C (1) 6. B (1) 7. A (1) 8. D (1) SECTION B 9. 3 3 + 7 = 3 3 7 3 3 7 3 3 + 7 6 3 7 = 7 7 6 3 7 3 3 7 0 10 = = 10. To find: (-1)³ + (7)³ + (5)³ Since

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

Ch 5 Practice Exam. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Ch 5 Practice Exam. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question. Name: Class: Date: Ch 5 Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the value of x. The diagram is not to scale. a. 32 b. 50 c.

More information

SUMMATIVE ASSESSMENT-1 SAMPLE PAPER (SET-2) MATHEMATICS CLASS IX

SUMMATIVE ASSESSMENT-1 SAMPLE PAPER (SET-2) MATHEMATICS CLASS IX SUMMATIVE ASSESSMENT-1 SAMPLE PAPER (SET-) MATHEMATICS CLASS IX Time: 3 to 3 1 hours Maximum Marks: 80 GENERAL INSTRUCTIONS: 1. All questions are compulsory.. The question paper is divided into four sections

More information

Examples: Identify three pairs of parallel segments in the diagram. 1. AB 2. BC 3. AC. Write an equation to model this theorem based on the figure.

Examples: Identify three pairs of parallel segments in the diagram. 1. AB 2. BC 3. AC. Write an equation to model this theorem based on the figure. 5.1: Midsegments of Triangles NOTE: Midsegments are also to the third side in the triangle. Example: Identify the 3 midsegments in the diagram. Examples: Identify three pairs of parallel segments in the

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

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

Indicate the answer choice that best completes the statement or answers the question.

Indicate the answer choice that best completes the statement or answers the question. Indicate the answer choice that best completes the statement or answers the question. ANIMATION Find the translation that moves the figure on the coordinate plane. Given the following information, determine

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

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

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

Page 1 of 8 Name: 1. Write in symbolic form the inverse of ~p q. 1. ~q p 2. q ~ p 3. p q 4. p ~ q 2. In symbolic form, write the contrapositive of p ~q. 1. q ~ p 2. ~p ~q 3. ~p q 4. ~q p 3. Figure 1 In

More information

Topic 2 [312 marks] The rectangle ABCD is inscribed in a circle. Sides [AD] and [AB] have lengths

Topic 2 [312 marks] The rectangle ABCD is inscribed in a circle. Sides [AD] and [AB] have lengths Topic 2 [312 marks] 1 The rectangle ABCD is inscribed in a circle Sides [AD] and [AB] have lengths [12 marks] 3 cm and (\9\) cm respectively E is a point on side [AB] such that AE is 3 cm Side [DE] is

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

2007 Fermat Contest (Grade 11)

2007 Fermat Contest (Grade 11) Canadian Mathematics Competition An activity of the Centre for Education in Mathematics and Computing, University of Waterloo, Waterloo, Ontario 007 Fermat Contest (Grade 11) Tuesday, February 0, 007 Solutions

More information

PRACTICE QUESTIONS CLASS IX: CHAPTER 4 LINEAR EQUATION IN TWO VARIABLES

PRACTICE QUESTIONS CLASS IX: CHAPTER 4 LINEAR EQUATION IN TWO VARIABLES PRACTICE QUESTIONS CLASS IX: CHAPTER 4 LINEAR EQUATION IN TWO VARIABLES 1. Find the value of k, if x =, y = 1 is a solution of the equation x + 3y = k.. Find the points where the graph of the equation

More information

DEPARTMENT OF MATHEMATICS

DEPARTMENT OF MATHEMATICS Wynberg Boys High School DEPARTMENT OF MATHEMATICS Name: Teacher: Class: PAPER 2 GRADE 9 MATHEMATICS JUNE 2017 MARKS: 75 TIME: 1 1 2 hours EXAMINER: Mr Biggs This examination booklet consists of 12 pages.

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

+2 u, 2s ) [D] ( r+ t + u, 2s )

+2 u, 2s ) [D] ( r+ t + u, 2s ) 1. Isosceles trapezoid JKLM has legs JK and LM, and base KL. If JK = 3x + 6, KL = 9x 3, and LM = 7x 9. Find the value of x. [A] 15 4 [] 3 4 [] 3 [] 3 4. Which best describes the relationship between the

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