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

 

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 1

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

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

 

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 3

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

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 3

 

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

 

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 4

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

Solution 4

 

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

 

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

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

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 6

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

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 6

SR is produced to meet PQ at E.

 

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

 

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 7

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

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 7

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

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

 

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency 

 

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

 

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 9

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

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 9

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 10

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

Solution 10

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 11

In a triangle ABC, if the bisectors of angles ABC and ACB meet at M then prove that: BMC = 90° + Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their CongruencyA.

Solution 11

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

 

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 12

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

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 12

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

 

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

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

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

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

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

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

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

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

 

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

 

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Chapter 11 - Triangles and their congruency Exercise Ex. 11.2

Question 1

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 1

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 5

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 5

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 7

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 7

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 8

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 8

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 9

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 9

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 10

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 10

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 11

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 11

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 12

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 12

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 13

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 13

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 14

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 14

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 15

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 15

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 17

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 17

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 19

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 19

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 20

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 20

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 21

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 21

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 23

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 23

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 24

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 24

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 25

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 25

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 26

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 26

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 27

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 27

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 28

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 28

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 29

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 29

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 30

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 30

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 31

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 31

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

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

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

 

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 3

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

 

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 3

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 4

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

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Solution 4

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency 

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

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

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

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 18

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

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

a. DDCE DLBE

b. AB = BL

c. Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency 

Solution 18

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Question 32

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

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

 

Solution 32

 

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency

Frank Solutions Icse Class 9 Mathematics Chapter - Triangles And Their Congruency