# Nozha Directorate of Education Form : 2 nd Prep

Size: px
Start display at page:

Transcription

1 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 two opposite sides are.., 2. In the //gram, each two consecutive angles are. 3. The //gram whose diagonals are perpendicular is called 4. The parallelogram whose diagonals are equal in length and perpendicular is called 5. The rhombus whose diagonals are equal in length is called. 6. The rectangle whose diagonals are perpendicular is called. 7. ABCD is a //gram in which m ( B ) = º 8. The two diagonals of the square are,.. 9. ABCD is a parallelogram in which m ( A ) + m ( C ) = 140 º 10. ABCD is a rectangle in which m ( A ) = 5x 10, then x = 2-Find The value of x, y and z :- 3-Find :- 1. The length of AM, BD, AD and BC 2. m ( A ), m ( B ) 4- in the opposite figure:- ABCD is a rectangle,fbce is a //gram Prove that : AF = DE 5- in the opposite figure:- ABCD, BEFC are two //grams Find m( ABE )

2 6- in the opposite figure :- Prove that ABCD is a //gram D A 110 C 70 B 7- in the opposite figure :- ABCD is a //gram in which BE = BC, DE = DC Prove that:- ABCD is a rectangle

3 Sheet 2 1- complete:- 1. The medians of the triangle intersect at 2. The no. of medians in the right angled triangle is 3. The length of the median from the vertex of the right angle in the right angled =. 4. The length of the hypotenuse in thirty and sixty triangle =.. the length of the side opposite the angle whose measure is 30 º 5. The line segment drawn between the two midpoints of two sides in a triangle is. And its length = 2- in the opposite figure :- DE = 4 cm, DM = 3 cm and BE = 6 cm Find the perimeter of BMC 3- in the opposite figure:- If m ( A ) = m ( D )= 90 º, M ( ACB ) = 30 º Prove that AB = DE 4- in the opposite figure :- Prove that YM = DE

4 5- in the opposite figure :- AB = DE Prove that m ( ADC ) = 90 º 6- in the opposite figure :- Prove that DFE is an isosceles 7- in the opposite figure :- Find the length of each of AB, XY and BZ

5 Sheet 3 Complete 1- In the isosceles if the measure of one of the two base angles 65º then the measure of its vertex angle = 2- In the isosceles if the vertex angle = 50 º then the measure of one of the two base angles =.. 3- If ABC is right angled at A, AB =AC then m ( B ) =.. 4- In XYZ if XY = XZ, then the exterior angle at the vertex Z is 5- In XYZ if XY = YZ = ZX, then m ( X ) =.º Find :- a) m ( D ) b) m ( CAD ) In the opposite figure :- AC = AB, CE = ED = CD Find m ( BCD ) Find :- m( MLY )

6 prove that :- AE bisects ( DAC ) Find the measure of the measures of the angles of ABC Find The value of X in the following figures:-

7 Sheet 4 Complete 1- If two angles in the triangle are congruent then the two sides opposite these two angles are and the triangle is. 2- If the three angles in the triangle are congruent then the triangle is 3- If the isosceles has angle = 45º, then the is 4- In ABC if AC = CB and m ( C ) m ( A ), then m ( B ) =.º 5- ABC is m ( A) = 30 º, m ( B ) : m ( C ) = 1 : 4 then ABC is 2- in the opposite figure :- MB=MC, AD // BC Prove that MA = MD 3- prove that AB = AC 4- in the opposite figure :- m( D ) = m ( E)=90º m( ABC) =m( ACB) Prove that m( DAB) = m( CAE)

8 5- BY=CZ, m ( B ) = m ( Z ) Prove that EYC is an isosceles 6- m( B) = ( C) find the perimeter of 7-ABCD is rectangle BF = CL Prove that: 1) AF = DL 2) EFL is an isosceles 8-ABCD is a square m ( MBC) = m ( MCB) Prove that AMD is an isosceles

9 9- m ( A ) = m ( B ), ED // AC ED = 2 1 AC Prove that :- m ( BEC ) = 90

10 Sheet 5 Complete 1- The straight line drawn from the vertex of the isosceles perpendicular to the base is called.. 2- The median of the isosceles drawn from the vertex. 3- The bisector of the vertex angle of the isosceles.. 4- The st. line drawn from the vertex of an isosceles its base 5- Any point the axis of the line segment is from its two terminals 6- If C the axis of symmetry of AB then = AC 7- The triangle whose angles are congruent has.. axes of symmetry 8- In ABC if m ( A ) = m ( B ) 60 then the no. of axes of symmetry of triangle ABC is 9- If the length of each sides in the triangle = 3 1 the perimeter of triangle then the no. of axes of symmetry of triangle is. 10- If ABCD is a rhombus then the axis of symmetry of AC is. 2- AB = AC, D and E are two midpoints of AB and AC Prove that 1- AM BC 2- AM bisects BAC 3-AC = AB, AB bisects BAC Prove that 1- BE = 2 1 BC 2- BC = CD

11 4-AD // BC, AE bisects BAD Prove that 1- AB =AD 2- AE BD 3- BE = ED 3- m ( ABD ) = m ( ACD ) AB = AC Prove that AD is the axis of symmetry of BC 4- AB = AC, BF bisects DBC, CF bisects BCE Prove that 1- BFC is an isosceles 2- AF is the axis of symmetry of BC

12 Sheet 6 1- Draw the isosceles triangle ABC which AB =AC using compasses, bisect BC at D. draw AD and prove that AD BC 2- Draw the equilateral ABC in which the length of each side is 4 cm then draw CD CB that intersect BA at D. find by proof length of AD 3- Draw ABC in which AB = 6 cm, m ( A ) = 50, m ( B ) = 70. Using the compasses and ruler draw XY passing through A and parallel to BC 4- Draw ABC with measure 60. bisect angle ABC from C draw CE // BA to meet the bisector of the angle at E, from E draw EF BA where EF BA = { F } prove that m ( ABC ) = m ( FEB ) 5- Draw any triangle bisect each B, C then draw AE // BC to meet the bisector of B at E and the bisector of C at F. prove that ABC is an isosceles triangle and FE = AB + AC

13 1- M bisects each of AC, BD Prove that m ( ABE) > m ( ACD) Sheet 7 2- AC > AB m ( AXY) = m( AYX) Prove that YC > XB 3- XY > XL, YZ > ZL Prove that m( XLZ) > m( XYZ) 4- AB = AC, BD > DC Prove that m( ABD) > m( ACD)

14 5- AB > AC, XY// BC Prove that m( AYX) > m(axy) 6- AB > AC BF bisects DBC CF bisects BCE Prove that m( FBC) > m( BCF) 7- prove that a) m ( ABC) > m ( ADC) b) m( BCD) > m( BAD) c) m( B) + m( C) > BM < AM Prove that ABC is an obtuse angle.

15 Sheet 8 1-Complete 1) The smallest angle of triangle (in measure ) is opposite to.. 2) The longest side in the right angle triangle is. 3) If triangle ABC m ( A) =50 m ( B) =30 4) If in triangle ABC m ( A) = m ( B) +m ( C) then the longest side in the triangle is.. 5) in the triangle ABC if m ( B) > m ( C) then.<. 2-AC CD, BD CD Prove that AB > CD 3- AB > AC, YX // BC XM bisects AYX Prove that XM > MY 4- AB = AD m( D ) > m( B ) prove that BC > CD

16 5- AB=BD=DF Prove that BC > A 6- prove that a) BD = DE b) DC > DB

17 Sheet 9 choose the correct answer :- 1-The lengths of any side in a triangle the sum of lengths of the two other sides a) > b) < c) = d) twice 2- Which of the following no. cannot be the lengths of sides of a triangle a) 7,7,5 b) 9,9,9 c) 3,6,12 d) 3, 4,5 3-If the lengths of two sides of an isosceles triangle are 3cm, 7cm then the length of the third side a) 7 cm b) 3 cm c) 4 cm d) 10 cm 4-In ABC AB + BC AC a) > zero b) < zero c) = zero d) = the perimeter of ABC 6-Is it possible to draw a triangle whose side length are as follows a) 5 cm, 7 cm, 8 cm b) 9 cm, 9 cm, 19 cm c) 5 cm, 3 cm, 4 cm Find the interval to which the length of the third side of :- a) 6 cm, 9 cm b) 5.7 cm, 7.3 cm c) 3 cm, 3 cm 1- prove that : MA + MB + MC > 2 1 the perimeter of ABC 2- ABCD is quadrilateral Prove that AB + BC + CD > AD

18

19

20

### 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

### 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 =..

### Unit (1) Numbers. 1) Complete : - 1) If x N then ( 2x + 1 ) is.( even or odd ) 2) If x N then 2 x is. = 3 , 2 = 3. 3) 3 2 x

Cairo Governorate Department : Maths Nozha Directorate of Education Form : 1 st Prep Nozha Language Schools Revision Sheet Ismailia Road Branch 1) Complete : - Unit (1) Numbers 1) If x N then ( 2x + 1

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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)

### Part (1) Second : Trigonometry. Tan

Part (1) Second : Trigonometry (1) Complete the following table : The angle Ratio 42 12 \ Sin 0.3214 Cas 0.5321 Tan 2.0625 (2) Complete the following : 1) 46 36 \ 24 \\ =. In degrees. 2) 44.125 = in degrees,

### 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?

### 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?

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

### 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

### 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

### 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

### 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)

### 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

### 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

### chapter 1 vector geometry solutions V Consider the parallelogram shown alongside. Which of the following statements are true?

chapter vector geometry solutions V. Exercise A. For the shape shown, find a single vector which is equal to a)!!! " AB + BC AC b)! AD!!! " + DB AB c)! AC + CD AD d)! BC + CD!!! " + DA BA e) CD!!! " "

### 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

### 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,

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

### 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,

### 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

### 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,

### 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

### 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

### 8. Quadrilaterals. If AC = 21 cm, BC = 29 cm and AB = 30 cm, find the perimeter of the quadrilateral ARPQ.

8. Quadrilaterals Q 1 Name a quadrilateral whose each pair of opposite sides is equal. Mark (1) Q 2 What is the sum of two consecutive angles in a parallelogram? Mark (1) Q 3 The angles of quadrilateral

### 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

### 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)

### 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

### 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

### Alg. Exercise (1) Department : Math Form : 1 st prep. Sheet. [1] Complete : 1) Rational number is 2) The set of integer is.. 3) If. is rational if x.

airo Governorate Nozha irectorate of Education Nozha Language Schools Ismailia Road epartment : Math Form : 1 st prep. Sheet [1] omplete : lg. Exercise (1) 1) Rational number is ) The set of integer is..

### 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

### LLT Education Services

8. The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle. (a) 4 cm (b) 3 cm (c) 6 cm (d) 5 cm 9. From a point P, 10 cm away from the

### 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

### 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

### 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

### 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 Thursday, January 27, 2011 9:15 a.m. to 12:15 p.m., only Student Name: School Name: Print your name and the name

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

### 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

### 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

### 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

### Grade 6 Math Circles March 22-23, 2016 Contest Prep - Geometry

Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 6 Math Circles March 22-23, 2016 Contest Prep - Geometry Today we will be focusing on how to solve

### HANOI OPEN MATHEMATICS COMPETITON PROBLEMS

HANOI MATHEMATICAL SOCIETY NGUYEN VAN MAU HANOI OPEN MATHEMATICS COMPETITON PROBLEMS 2006-2013 HANOI - 2013 Contents 1 Hanoi Open Mathematics Competition 3 1.1 Hanoi Open Mathematics Competition 2006...

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### triangles in neutral geometry three theorems of measurement

lesson 10 triangles in neutral geometry three theorems of measurement 112 lesson 10 in this lesson we are going to take our newly created measurement systems, our rulers and our protractors, and see what

### 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

### (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

### 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

### 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

### 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

### 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

### KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 01 F PERIODIC TEST III EXAM (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS IX Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks)

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

### 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

### 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

### 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

### 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

### G.CO.6-9 ONLY COMMON CORE QUESTIONS

Class: Date: G.CO.6-9 ONLY COMMON CORE QUESTIONS Multiple Choice Identify the choice that best completes the statement or answers the question. 1 The image of ABC after a rotation of 90º clockwise about

### INSTRUCTIONS. F.3 2 nd Maths Examination (1011) P1/14

INSTRUCTIONS 1. The total mark of this paper is 100. 2. This paper consists of THREE sections, A, B and C. 3. Attempt ALL questions in this paper. Write your answers in the spaces provided in this Question-Answer

### 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

### 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.

### 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

### 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

### 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

### SUMMATIVE ASSESSMENT - I (2012) MATHEMATICS CLASS IX. Time allowed : 3 hours Maximum Marks :90

SUMMATIVE ASSESSMENT - I (2012) MATHEMATICS CLASS IX Time allowed : 3 hours Maximum Marks :90 General Instructions: i. All questions are compulsory. ii. The question paper consists of 34 questions divided

### Year 9 Term 3 Homework

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

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

### 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,

### 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

### 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

### 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

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

### 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

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

### 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

### RMT 2013 Geometry Test Solutions February 2, = 51.

RMT 0 Geometry Test Solutions February, 0. Answer: 5 Solution: Let m A = x and m B = y. Note that we have two pairs of isosceles triangles, so m A = m ACD and m B = m BCD. Since m ACD + m BCD = m ACB,

### 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

### b) What is the area of the shaded region? Geometry 1 Assignment - Solutions

Geometry 1 Assignment - Solutions 1. ABCD is a square formed by joining the mid points of the square PQRS. LKXS and IZXY are the squares formed inside the right angled triangles DSC and KXC respectively.

### 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

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

Name: Regents Review Session Two Date: Common Core Geometry 1. The diagram below shows AB and DE. Which transformation will move AB onto DE such that point D is the image of point A and point E is the

### 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

### 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

### 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

### Revision Question Bank

Revision Question Bank Triangles 1. In the given figure, find the values of x and y. Since, AB = AC C = B [angles opposite to the equal sides are equal] x = 50 Also, the sum of all angles of a triangle