# 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.

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

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

a. ∠Q

b. ∠R

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

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

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

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.

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

SR is produced to meet PQ at E.

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

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°.

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

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

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

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

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.

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

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

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.

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

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.

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

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

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

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.

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.

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

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