## Chapter 16 - Similarity Exercise Ex. 16.1

Question 1
The sides PQ and PR of thePQR are produced to S and T respectively. ST is drawn parallel to QR and PQ: PS = 3:4. If PT = 9.6 cm, find PR. If 'p' be the length of the perpendicular from P to QR, find the length of the perpendicular from P to ST in terms of 'p'.
Solution 1

Question 2
In a quadrilateral PQRS, the diagonals PR and QS intersect each other at the point T. If PT:TR = QT :TS = 1:2, show that
PTQ - DRTS
Solution 2
Question 3
In a quadrilateral PQRS, the diagonals PR and QS intersect each other at the point T. If PT:TR = QT :TS = 1:2, show that
TP:TQ = TR:TS
Solution 3
Question 4
In the given figure, PB is the bisector ofABC andABC =ACB. Prove that:
a. BC x AP = PC x AB
b. AB:AC = BP: BC

Solution 4

Question 5
In a right-angled triangle ABC,B = 90°, P and Q are the points on the sides AB and AC such as PQBC, AB = 8 cm, AQ = 6 cm and PA:AB = 1:3. Find the lengths of AC and BC.
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

## Chapter 16 - Similarity Exercise Ex. 16.2

Question 1
Given that name the corresponding angles and the corresponding sides.
Solution 1
Question 2
InBC such that AD =1.5 cm, DB = 3 cm and AE = 1 cm. Find AC.
Solution 2

Question 3
Given is a triangle with sides 3 cm, 5 cm and 6 cm. Find the sides of a triangle which is similar to the given triangle and its shortest side is 4.5 cm.
Solution 3
Question 4
Two figures are similar. If the ratio of their perimeters is 8:16. What will be the ratio of the corresponding sides?
Solution 4
Question 5
Harmeet is 6 feet tall and casts a shadow of 3 feet long. What is the height of a nearby pole if it casts a shadow of 12 feet long at the same time?
Solution 5
Question 6
In a triangle ABC, AB = 4 cm, BC = 4.5 cm and CA = 5 cm. ConstructABC. Find the image A'B'C of theABC obtained by enlarging it by a scale factor 2. Measure the sides of the image A'B'C' and show that
AB:A'B' = AC:B'C' = CA:C'A'
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