# FRANK Solutions for Class 9 Maths Chapter 11 - Triangles and their congruency

Learn to use the exterior angle property confidently in your exam with the help of TopperLearning’s Frank Solutions for ICSE Class 9 Mathematics Chapter 11 Triangles and their Congruency. Revise the steps to use the Angle-Side-Angle criteria or Side-Angle Side criteria with our model answers.

Also, practise the proofs given in our ICSE Class 9 Math Frank textbook solutions to understand how to explain the relation between two triangles or two line segments. In addition, grasp how to solve questions related to congruent triangles in this chapter. Further, for Maths self-study, watch our videos by experts and then evaluate your exam-preparedness with our online practice tests.

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## Chapter 11 - Triangles and their congruency Exercise Ex. 11.1

Question 1

In the given figure, Q : R = 1 : 2. Find:

a. Q

b. R

Solution 1

Question 2

The exterior angles, obtained on producing the side of a triangle both ways, are 100° and 120°. Find all the angles of the triangle.

Solution 2

Question 3

Use the given figure to find the value of x in terms of y. Calculate x, if y = 15°.

Solution 3

Question 4

In a triangle PQR, P + Q = 130° and P + R = 120°. Calculate each angle of the triangle.

Solution 4

Question 5

The angles of a triangle are (x + 10)°, (x + 30)° and (x - 10)°. Find the value of 'x'. Also, find the measure of each angle of the triangle.

Solution 5

Question 6

Use the given figure to find the value of y in terms of p, q and r.

Solution 6

SR is produced to meet PQ at E.

Question 7

In the figure given below, if RS is parallel to PQ, then find the value of y.

Solution 7

Question 8

In a triangle PQR, the internal bisectors of angles Q and R meet at A and the external bisectors of the angles Q and R meet at B. Prove that: QAR + QBR = 180°.

Solution 8

Question 9

Use the given figure to show that: p + q + r = 360°.

Solution 9

Question 10

In a triangle ABC. If D is a point on BC such that CAD = B, then prove that: ADC = BAC.

Solution 10

Question 11

In a triangle ABC, if the bisectors of angles ABC and ACB meet at M then prove that: BMC = 90° + A.

Solution 11

Question 12

If bisectors of angles A and D of a quadrilateral ABCD meet at 0, then show that B + C = 2 AOD

Solution 12

Question 13

If each angle of a triangle is less than the sum of the other two angles of it; prove that the triangle is acute-angled.

Solution 13

Question 14

If the angles of a triangle are in the ratio 2 : 4 : 6; show that the triangle is a right-angled triangle.

Solution 14

Question 15

In a triangle, the sum of two angles is 139° and their difference is 5°; find each angle of the triangle.

Solution 15

Question 16

In a right-angled triangle ABC, B = 90°. If BA and BC produced to the points P and Q respectively, find the value of PAC + QCA.

Solution 16

## Chapter 11 - Triangles and their congruency Exercise Ex. 11.2

Question 1

Solution 1

Question 5

Solution 5

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 17

Solution 17

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26

Question 27

Solution 27

Question 28

Solution 28

Question 29

Solution 29

Question 30

Solution 30

Question 31

Solution 31

Question 2

A is any point in the angle PQR such that the perpendiculars drawn from A on PQ and QR are equal. Prove that AQP = AQR.

Solution 2

Question 3

In the given figure P is a midpoint of chord AB of the circle O. prove that OP ^ AB.

Solution 3

Question 4

In a circle with center O. If OM is perpendicular to PQ, prove that PM = QM.

Solution 4

Question 6

In a triangle ABC, if D is midpoint of BC; AD is produced upto E such as DE = AD, then prove that:

a. DABD and DECD are congruent.

b. AB = EC

c. AB is parallel to EC

Solution 6

Question 16

If the perpendicular bisector of the sides of a triangle PQR meet at I, then prove that the line joining from P,Q,R to I are equal.

Solution 16

Question 18

In the given figure ABCD is a parallelogram, AB is Produced to L and E is a midpoint of BC. Show that:

a. DDCE DLBE

b. AB = BL

c.

Solution 18

Question 32

In the given figure, AB = DB and AC = DC. Find the values of x and y.

Solution 32

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