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

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

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 1

Question 2

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

Solution 2

Question 3

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

Solution 3

 

Question 4

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 4

Question 5

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 5

Question 6

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 6

Question 7

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

Solution 7

Question 8

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Question 9

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Question 10

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Question 11

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Question 12

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Question 13

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Question 14

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Question 15

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Question 16

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Question 17

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Question 18

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Question 19

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Question 20

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Question 21

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Question 22

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Question 23

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Question 24

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Question 25

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Question 26

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Question 27

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Question 28

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Question 29

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Question 30

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Question 31

Solution 31