# 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.

### Solution 2

(i) False

(ii) True

(iii) False

(iv) False

(v) True

(vi) True

## Triangles Exercise Ex. 7.2

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## Triangles Exercise Ex. 7.3

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## Triangles Exercise Ex. 7.4

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## Triangles Exercise Ex. 7.5

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**We have: **

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## Triangles Exercise Ex. 7.6

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** **

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 is90^{o})

AOP = DOM (vertically opposite angles)

OAP = ODM (remaining angle)

Therefore APO ~ DMO (By AAA rule)

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### 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

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** ****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.**

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**(i)**

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**(i) **

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## Triangles Exercise Rev. 7

### Solution 1(i)

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### Solution 7(i)

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

### Solution 7(v)

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

### Solution 7(vi)

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**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 a^{2}b^{2}

According to question, ratio of sides= 4:9

Hence ratio of areas = 4^{2}:9^{2}

= 16:81

So, the correct option is (d).

### Solution 2

So, the correct option is (a).

### Solution 3

## Triangles Exercise 7.132

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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 = 2^{2}:5^{2 }

= 4:25

So, the correct option is (b).

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## Triangles Exercise 7.133

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For triangles to be similar by SAS

∠B = ∠D

So, the correct option is (c).

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So, the correct option is (a).

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So, the correct option is (b).

### Solution 25

So, the correct option is (c).

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So, the correct option is (c).

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So, the correct option is (b).

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## Triangles Exercise 7.134

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So, the correct option is (b).

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## Triangles Exercise 7.135

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So, the correct option is (a).

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So, the correct option is (b).

## Triangles Exercise 7.136

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