# Revision Question Bank

Size: px
Start display at page:

Transcription

1 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 is x + y= y = 180 [put x = 50 ] y= = 80 Hence, x = 50 and y = In the given figure, PQ > PR, QS and RS are the bisectors of Q and R, respectively. Then, prove that SQ > SR Given, PQ > PR PRQ > PQR [angle opposite to the longer angle is longer] 1 2 PRO > 1 2 PQR [dividing both sides by 2] SRQ > SQR SQ > SR [side opposite to the longer angle is longer] S.C.O , Sector 40 D, CHD. Phone: ,

2 3. In the given figure, BA AC,DE DF such that BA=DE and BF = EC. Show that ABC DEF In ABC and DEF, BA =DE BF = EC BF + FC = EC + CF [adding both sides by FC] BC = EF Also, CAB = FDF [each 90 ] ABC DEF [by RHS congruence rule] 4. In figure, AB = DE, BC=EF and median AP = median DQ. Prove that B = E. Given ABC and DEF in which AB = DE, BC = EF and median AP = median DQ. To prove B = E Proof BC = EF 1 1 BC EF 2 2 [dividing both sides by 2] BP = EQ [ AP and DQ are medians] In ABP and DEQ, AB = DE AP=DQ and BP = EQ [proved above] S.C.O , Sector 40 D, CHD. Phone: ,

3 ABP DEQ [by SSS congruence rule] B = E [by CPCT] Hence proved. 5. Show that a median of a triangle divides it into two triangles of equal areas. Given ABC in which AD is the median i.e., BD = CD To prove ar( ABD) = ar( ACD) Construction Draw AE BC Proof ar( ABD) 1 2 and ar ( ACD) = 1 2 BD AE...(i) CD AE = 1 2 BD AE...(ii) [ CD = BD, given] From Eqs. (i) and (ii), we get ar( ABD) = ar( ACD) Hence proved. 6. In the given figure, XYZ and PYZ are two isosceles triangles on the base YZ with XY = XZ and PY= PZ. If P=120 and XYP=40, then find YXZ. Given, in PXZ, PY = PZ PZY = PYZ [opposite angles of equal sides are equal] S.C.O , Sector 40 D, CHD. Phone: ,

4 Let PYZ = PZY =x P + PYZ + PZY = 180 [ the sum of all angles of a triangle is 180 ] 120 +x + x = 180 2x = x = 60 x = 30 PYZ = PZY = 300 Now, XYZ = XYP + PYZ = = 70 In XYZ, YXZ + XYZ + XZY = 180 [ sum of all angles of a triangle is 180 ] YXZ = 180 YXZ = = In a right angled triangle, one acute angle is double the other. Prove that the hypotenuse is double the smallest side. We have, AABC in which B is right angle and C is double A. Produce CB upto D such that BC = BD and join AD. In ABD and ABC, BD = BC [by construction] ABD = ABC [each 90 ] and AB = AB [common side] ABD ABC [ by SAS Congruence rule] AD = AC and DAB = CAB = x [CPCT] [by CPCT] S.C.O , Sector 40 D, CHD. Phone: ,

5 Now, DAC = DAB + CAB DAC = x + x = 2x DAC = ACB [ ACB = 2x] DC = AD [ sides opposite to equal angles are equal] 2BC = AD = AC [ BC = DB] Hence proved. 8. In the given figure, RS = QT and QS=RT. Prove that PQ =PR. Given In PQR, RS = QT and QS = RT To prove PQ = PR Proof In RESQ and QTR, RS = QT.. (i) SQ = RT..(ii) and RQ = RQ...(iii) [common side] RSQ QTR [by SSS congruence rule] QRS = RQT...(i) [by CPCT] and QRT = RQS [by CPCT]...(ii) On subtracting Eq. (ii) from Eq. (i), we get QRS QRT = RQT RQS TRS = SQT Also, RSQ = QTR On multiplying both sides by -1 and then adding 180, we get 180 RSQ =180 QTR QSP = RTP RPT QPS [by ASA congruence rule] PQ = PR Hence proved. 9. ABC is a triangle in which B = 2 C. D is a point on side BC such that AD bisects BAC and AB = CD. Prove that BAC=72. S.C.O , Sector 40 D, CHD. Phone: ,

6 Given B = 2 C AD is the bisector of A and AB = DC To prove BAC =72 Construction Draw BE as angle bisector of B. Join DE. If C = x, then ABE = EBC = x Proof Since, AD is the bisector of A. BAD = CAD = y [let] Now, EBC is. an isosceles triangle. So, EBC = ECB= x EB = EC Consider ABE DCE [by SAS congruence rule] EDC = 2y [by CPCT]...(i) Consider isosceles AED as EA = ED EA = ED [by CPCT] LDA = EAD = y... (ii) From Eqs. (i) and (ii), we get ADC = y + 2y =3y... (iii) or ADC = 2x + y... (iv) [exterior angles of AABD ] From Eqs. (iii) and (iv), we get 3y = 2x + y x = y...(v) Now, in ABC, A + B + C=180 [ sum of all angles of a triangle is 180 ) 2y + 2x + x =180 2y + 2y + y = 180 [from Eq. (v)] 5y = y S.C.O , Sector 40 D, CHD. Phone: ,

7 A = 2y = 2 36 = 72 Hence, BAC = 72 Hence proved. 10. In the given figure, if E > A, C > D, then AD > EC. Is it true? True, In AEB, E > A AB > BE...(i) In BDC, C > D BD > BC...(ii) On adding Eqs. (i) and (ii), we get AB + BD > BE + BC AD > EC Chapter Test {Triangles} M: Marks: 40 M: Time: BE and CF are two equal altitudes of a ABC. Using RHS congruence rule, prove that ABC is an isosceles triangle. [4] Given In a ABC, BE and CF are two equal altitudes of a ABC. To prove ABC is an isosceles triangle. S.C.O , Sector 40 D, CHD. Phone: ,

8 Proof In ABC and CFB, BE=CF [given, equal altitudes] BEC = CFB [each 90 ] and BC = BC [common side] BEC CFB [by RHS congruence rule] ECB = FBC [by CPCT] or ACB = ABC Hence proved. 2. In figure, S is any point on the side QR of PQR. Prove that PQ + QR+ RP>2PS. [4] We know that, sum of the two sides of a triangle is greater than the third side. In PQS, PQ + QS>PS...(i) and in PRS, PR + SR>PS...(ii) On adding Eqs. (i) and (ii), we get (PQ + QS) + (PR + SR)> 2PS PQ + (QS + SR) +PR > 2PS PQ + QR + RP>2PS Hence proved. 3. In figure, AB = AC, D is a point in the interior of ABC such that DBC = DCB. Prove that AD bisects BAC of ABC. [4] S.C.O , Sector 40 D, CHD. Phone: ,

10 students without any religion bias. 5. In the adjoining figure, ABC is a triangle and D is any point in its interior. Show that BD + DC < AB + AC. [4] Produced BD to meet AC in E. In ABE, AB + AE>BE [ sum of two sides is greater than the third side] AB+AE > BD + DE...(i) [ BE =BD + DE] In CDE, DE + EC > DC...(ii) [ sum of two sides is greater than the third side] On adding Eqs. (i) and (ii), we get AB + AE +DE +EC > BD + DE + DC AB + (AE +EC)>BD + DC AB + AC>BD + DC Hence, BD + DC < AB + AC 6. In ABC, if AD is the bisector of A, then show that AB > BD and AC > DC. [4] Solution : In ABC, AD is the bisector of A 1 = 2..(i) Since exterior angle of a triangle is greater than each of interior opposite angle. Therefore, in ADC, we have Ext. ADC > 2 3 > 2 3 > 1 [Using (i)] Thus, in ABD, we have 3 > 1 AB >BD [Side opp, to greater angle is larger] S.C.O , Sector 40 D, CHD. Phone: ,

11 Hence, AB > BD. Similarly, we can prove that AC < CD. 7. In the given figure, PQR is an equilateral triangle and QRST is a square. Prove that (i) PT = PS (ii) PSR = 15 [4] Solution Given : QRST is a square and PQR is an equilateral triangle. To prove : (i) PS = PS (ii) PSR = 15 0 Proof : Since QRST is a square and PQR is an equilateral triangle. TQR = 90 0 and PQR = 60 0 TQR + PQR = TQP = Thus, in TQP and SRP, we have TQ = RS TQP = SRP = and QP = RP TQP SRP (by SAS congruence criteria) PT = PS (by cpct) (ii) In PSR SR = RP ( QR = SR) RPS = PSR = x (say) Now, RPS + PSR + SRP = x + x = x = x = (by angle sum property) S.C.O , Sector 40 D, CHD. Phone: ,

12 2x = 30 0 x = 15 0 PSR = A plot is in the form of AEF. Owner of this plot wants to build old age home, health centre and dispensary for elderly people as shown in figure. In which ABCD is a parallelogram and AB = BE and AD = DF. (i) Prove that BEC DCF. (ii) What values are depicted here? [4] Solution : Given : ABCD is a parallelogram AB = BE and AD = DF To prove : BEC DCF Proof : Since ABCD is a parallelogram AB = DC But AB = BE (given) DC = BE Also, AD = BC but AD = DF (given) BC = DF As ABCD is a parallelogram,..(i)..(ii) S.C.O , Sector 40 D, CHD. Phone: ,

13 AD BC and AE as a transversal, 1 = 2 (corresponding angles)..(iii) Also, AB DC and AF as a transversal, 1 = 3 (corresponding angles)..(iv) from (iii) and (iv), we get 2 = 3..(v) Therefore, in BEC and DCF, we have BE = DC (from (i) BC = DF (from (ii) 2 = 3 (from (v) BEC DCF (by SAS congruence rule) (ii) Kindness and respectful for elder people. 9. In the figure, ABCD is a quadrilateral in which AD = BC and DAB = CBA. [4] Prove that (i) ABD BAC (ii) BD = AC Solution : Given : AD = BC and DAB = CBA To prove : (i) ABD ABC (ii)bd = AC Proof : In ABD and BAC, we have : AD = BC (Given) DAB = CBA (Given) AB = AB (common) Therefore, ABD BAC (by SAS congruence rule) (ii) BD = AC (by cpct) 10. ABCD is a square. P and Q are points on DC and BC respectively, such that AP = DQ, prove that (i) ADP DCQ (ii) DMP = 90 [4] S.C.O , Sector 40 D, CHD. Phone: ,

14 Solution : Given : ABCD is a square, AP = AQ To prove : (i) ADP DCQ (ii) DMP = 90 0 Proof : (i) In ADP and DCQ ADP = DCQ = 90 0 AP = DQ (Given) AD = CD ( ABCD is a square) ADP DCQ A (by RHS congruence rule) (ii) Since ADP DCQ (by (i)) DAP + DAP + DPA = (by angle sum property) DAP + DPA = DAP + DPA = 90 0 QDC + DPA = 90 0 MDP + DPM = 900 In MDP, MDP + DPM + PMD = PMD = PMD = PMD = 90 0 (by (i)).. (ii) (by angle sum property by ii) S.C.O , Sector 40 D, CHD. Phone: ,

15 S.C.O , Sector 40 D, CHD. Phone: ,

### 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

### 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)

### 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

### 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

### 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

### 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

### 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,

### 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

### Class-IX CBSE Latest Pattern Sample Paper {Mathematics}

Class-IX CBSE Latest Pattern Sample Paper {Mathematics} Term-I Examination (SA I) Time: 3hours Max. Marks: 90 General Instructions (i) All questions are compulsory. (ii) The question paper consists of

### 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

### 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

### 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

### 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?

### 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.

### 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

### 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

### 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

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

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

### 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

### 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

### 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

### 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

### SHW 1-01 Total: 30 marks

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

### 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

### IB MYP Unit 6 Review

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

### 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

### 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

### Class IX Chapter 6 Lines and Angles Maths. Exercise 6.1. In the given figure, lines AB and CD intersect at O. If

Question 1: Exercise 6.1 In the given figure, lines AB and CD intersect at O. If and find BOE and reflex COE. Question 2: In the given figure, lines XY and MN intersect at O. If POY = and a:b = 2 : 3,

### Class IX Chapter 6 Lines and Angles Maths

Class IX Chapter 6 Lines and Angles Maths Exercise 6.1 Question 1: In the given figure, lines AB and CD intersect at O. If and find BOE and reflex COE. Question 2: 2 In the given figure, lines XY and MN

### 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

### 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

### 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

### 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

### Chapter 8 Similar Triangles

Chapter 8 Similar Triangles Key Concepts:.A polygon in which all sides and angles are equal is called a regular polygon.. Properties of similar Triangles: a) Corresponding sides are in the same ratio b)

### Review for Geometry Midterm 2015: Chapters 1-5

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

### 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

### 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.

### 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,

### 3. AD is a diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm, the distance of AB from the centre of the circle is:

Solved Paper 2 Class 9 th, Mathematics, SA 2 Time: 3hours Max. Marks 90 General Instructions 1. All questions are compulsory. 2. Draw neat labeled diagram wherever necessary to explain your answer. 3.

### 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

### 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

### 6 LINES AND ANGLES EXERCISE 6.1. Q.1. In the figure lines AB and CD intersect at O. If AOC + BOE = 70 and BOD = 40, find BOE and reflex COE.

6 LINES AND ANGLES EXERCISE 6.1 Q.1. In the figure lines AB and CD intersect at O. If AOC + BOE = 70 and BOD = 40, find BOE and reflex COE. Sol. Lines AB and CD intersect at O. AOC + BOE = 70 (Given) (1)

### 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

### 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

### 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

### RD Sharma Solutions for Class 10 th

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

### 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

### BOARD QUESTION PAPER : MARCH 2016 GEOMETRY

BOARD QUESTION PAPER : MARCH 016 GEOMETRY Time : Hours Total Marks : 40 Note: (i) Solve All questions. Draw diagram wherever necessary. (ii) Use of calculator is not allowed. (iii) Diagram is essential

### 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

### 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

### 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

### 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

### 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

### 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

### JEFFERSON MATH PROJECT REGENTS AT RANDOM

JEFFERSON MATH PROJECT REGENTS AT RANDOM The NY Geometry Regents Exams Fall 2008-August 2009 Dear Sir I have to acknolege the reciept of your favor of May 14. in which you mention that you have finished

### 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

### V15PCAF I, 2013 SUMMATIVE ASSESSMENT I, 2013 / MATHEMATICS IX / Class IX

V15PCAF I, 01 SUMMATIVE ASSESSMENT I, 01 / MATHEMATICS IX / Class IX 90 Time Allowed : hours Maximum Marks : 90 General Instructions: All questions are compulsory. 1 1 6 10 11 The question paper consists

### 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

### MT EDUCARE LTD. SUMMATIVE ASSESSMENT Roll No. Code No. 31/1

CBSE - X MT EDUCARE LTD. SUMMATIVE ASSESSMENT - 03-4 Roll No. Code No. 3/ Series RLH Please check that this question paper contains 6 printed pages. Code number given on the right hand side of the question

### JEFFERSON MATH PROJECT REGENTS AT RANDOM

JEFFERSON MATH PROJECT REGENTS AT RANDOM The NY Geometry Regents Exams Fall 2008-January 2010 Dear Sir I have to acknolege the reciept of your favor of May 14. in which you mention that you have finished

### 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

### 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

### CONGRUENCE AND SIMILARITY

CONGRUENCE ND SIMILRITY 1.1CONGRUENT FIGURES The figures that have the same size and the same shape, i.e. one shape fits exactly onto other is called Congruent figures. CONGRUENT TRINGLES: 1. Two triangles

### 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

### 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

### 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

### Maharashtra State Board Class X Mathematics Geometry Board Paper 2015 Solution. Time: 2 hours Total Marks: 40

Maharashtra State Board Class X Mathematics Geometry Board Paper 05 Solution Time: hours Total Marks: 40 Note:- () Solve all questions. Draw diagrams wherever necessary. ()Use of calculator is not allowed.

### 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)

### 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

### 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

### Name: Class: Date: If AB = 20, BC = 12, and AC = 16, what is the perimeter of trapezoid ABEF?

Class: Date: Analytic Geometry EOC Practice Questions Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In the diagram below of circle O, chords AB and CD

### 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

### 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

### 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

### 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.

### 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

### Solution 1: (i) Similar (ii) Similar (iii) Equilateral (iv) (a) Equal (b) Proportional

Class X - NCERT Maths EXERCISE NO: 6.1 Question 1: Fill in the blanks using correct word given in the brackets: (i) All circles are. (congruent, similar) (ii) All squares are. (similar, congruent) (iii)

### 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

### CBSE MATHEMATICS (SET-2)_2019

CBSE 09 MATHEMATICS (SET-) (Solutions). OC AB (AB is tangent to the smaller circle) In OBC a b CB CB a b CB a b AB CB (Perpendicular from the centre bisects the chord) AB a b. In PQS PQ 4 (By Pythagoras

### 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

### 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

### 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

### Practice Test Student Answer Document

Practice Test Student Answer Document Record your answers by coloring in the appropriate bubble for the best answer to each question. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

### 1 / 23

CBSE-XII-017 EXAMINATION CBSE-X-008 EXAMINATION MATHEMATICS Series: RLH/ Paper & Solution Code: 30//1 Time: 3 Hrs. Max. Marks: 80 General Instuctions : (i) All questions are compulsory. (ii) The question

### 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'

### 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

### 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

### 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

### CLASS IX MID TERM EXAMINATION ( ) Subject: MATHS SOLUTIONS. Set B-2. TIME :3hrs MAX.MARKS: 80

CLASS IX MID TERM EXAMINATION (017-18) Subject: MATHS SOLUTIONS Set B- TIME :hrs MAX.MARKS: 80 General Instructions:Do not copy any question.make a rough figure wherever needed. Section- A contains Q 1.

### Geometry Essentials ( ) Midterm Review. Chapter 1 For numbers 1 4, use the diagram below. 1. Classify as acute, obtuse, right or straight.

Geometry Essentials (2015-2016) Midterm Review Name: Chapter 1 For numbers 1 4, use the diagram below. 1. Classify as acute, obtuse, right or straight. 2. is a linear pair with what other angle? 3. Name

### 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

### 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

### Mathematics. Exercise 6.4. (Chapter 6) (Triangles) (Class X) Question 1: Let and their areas be, respectively, 64 cm 2 and 121 cm 2.

() Exercise 6.4 Question 1: Let and their areas be, respectively, 64 cm 2 and 121 cm 2. If EF = 15.4 cm, find BC. Answer 1: 1 () Question 2: Diagonals of a trapezium ABCD with AB DC intersect each other

### CBSE Class IX Mathematics Term 1. Time: 3 hours Total Marks: 90. Section A

CBSE sample papers, Question papers, Notes for Class 6 to 1 CBSE Class IX Mathematics Term 1 Time: 3 hours Total Marks: 90 General Instructions: 1. All questions are compulsory.. The question paper consists

### 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)

### Answers. Chapter 9 A92. Angles Theorem (Thm. 5.6) then XZY. Base Angles Theorem (Thm. 5.6) 5, 2. then WV WZ;

9 9. M, 0. M ( 9, 4) 7. If WZ XZ, then ZWX ZXW ; Base Angles Theorem (Thm..6). M 9,. M ( 4, ) 74. If XZ XY, then XZY Y; Base Angles Theorem (Thm..6). M, 4. M ( 9, ) 7. If V WZV, then WV WZ; Converse of