Chapter 11 : Triangles and their congruency - Frank Solutions for Class 9 Maths ICSE

Mathematics in ICSE Class 9 is one of the most challenging and trickiest subjects of all. It includes complex topics such as logarithms, expansions, indices and Pythagoras Theorem which are difficult to understand for an average student. TopperLearning provides study materials for ICSE Class 9 Mathematics to make the subject easy and help students to clear all their concepts. Our study materials comprise numerous video lessons, question banks, revision notes and sample papers which help achieve success in the examination.

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Chapter 11 - Triangles and their congruency Excercise 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 Excercise Ex. 11.2

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

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 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

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 25

 

Question 26

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

 

Solution 26

Question 27

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

Solution 27

 

Question 28

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 28

Question 29

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 29

Question 30

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 30

Question 31

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

 

Solution 31

 

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