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# Class 10 RD SHARMA Solutions Maths Chapter 7 - Triangles

## Triangles Exercise Ex. 7.1

### Solution 1

(i) All circles are similar.
(ii) All squares are similar.
(iii) All equilateral triangles are similar.

(iv) Two triangles are similar, if their corresponding angles are equal.

(v) Two triangles are similar, if their corresponding sides are proportional.
(vi) Two polygons of the same number of sides are similar, if (a) their corresponding angles are equal and (b) their corresponding sides are proportional.

(i) False

(ii) True

(iii) False

(iv) False

(v) True

(vi) True

We have:

## Triangles Exercise Ex. 7.6

### Solution 19

Since ABC and DBC are one same base,
Therefore ratio between their areas will be as ratio of their heights.
Let us draw two perpendiculars AP and DM on line BC.

In APO and DMO,
APO = DMO    (Each is90o)
AOP = DOM          (vertically opposite angles)
OAP = ODM         (remaining angle)
Therefore APO ~  DMO    (By AAA rule)

### Solution 18

In trapezium PQRS, PQ || RS and PQ = 3RS.

… (i)

In POQ and ROS,

SOR = QOP … [Vertically opposite angles]

SRP = RPQ … [Alternate angles]

∴ ∆POQ ROS … [By AA similarity criteria]

Using the property of area of areas of similar triangles, we have

Hence, the ratio of the areas of triangles POQ and ROS is 9:1.

## Triangles Exercise Ex. 7.7

### Solution 5

Let CD and AB be the poles of height 11 and 6 m.
Therefore CP = 11 - 6 = 5 m
From the figure we may observe that AP = 12m
In triangle APC, by applying Pythagoras theorem

Therefore distance between their tops = 13 m.

(i)

(i)

## Triangles Exercise Rev. 7

### Solution 7(iv)

Incomplete question (two triangles are not given in the figure).

### Solution 7(v)

Incomplete question (two triangles are not given in the figure).

### Solution 38

The given information can be represented by the figure given below.

## Triangles Exercise 7.131

### Solution 1

We know if sides of two similar triangles are in ratio a:b then area of these triangles are in ratio a2b2

According to question, ratio of sides= 4:9

Hence ratio of areas = 42:92

= 16:81

So, the correct option is (d).

### Solution 2

So, the correct option is (a).

## Triangles Exercise 7.132

### Solution 6

All these pairs of corresponding sides are in the same proportion so by SSS similarity criteria triangle ∆ABC are similar.

Given ratio of sides = 2.5

So, ratio of areas    = 22:52

= 4:25

So, the correct option is (b).

## Triangles Exercise 7.133

### Solution 19

For triangles to be similar by SAS

∠B = ∠D

So, the correct option is (c).

### Solution 21

So, the correct option is (a).

### Solution 24

So, the correct option is (b).

### Solution 25

So, the correct option is (c).

### Solution 27

So, the correct option is (c).

### Solution 28

So, the correct option is (b).

## Triangles Exercise 7.134

### Solution 31

So, the correct option is (b).

## Triangles Exercise 7.135

### Solution 37

### Solution 39

So, the correct option is (a).

### Solution 40

So, the correct option is (b).

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