## 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
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
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