## Properties of Triangle

Properties of triangle are discussed here:

## Property 1:

The sum of three angles of a triangle equals to 180°.

In each case, **the sum of the measures of angles equals to 180°**. So if two angles of a triangle are given, we can easily find out its third angle.

**For Example:**

**1.** In a right triangle, if one angle is 50°, find its third angle.

*Solution:*

∆ PQR is a right triangle, that is, one angle is right angle.

Given, ∠PQR = 90°

∠QPR = 50°

Therefore, ∠QRP = 180° - (∠Q + ∠ P)

= 180° - (90° + 50°)

= 180° - 140°

∠ R = 40°

## Property :

The sum of the length of any two sides of a triangle is greater than the length of the third side.

In each case, if we add up any two sides of the ∆, the sum is more than its third side.

**For Example:**

**1.** Is it possible to have a triangle whose sides are 5 cm, 6 cm and 4 cm?

*Solution:*

The lengths of the sides are 5 cm, 6 cm, 4 cm,

(a) 5 cm + 6 cm > 4 cm.

(b) 6 cm + 4 cm > 5 cm.

(c) 5 cm + 4 cm > 6cm.

Hence, a triangle with these sides is possible.

**2.** Is the construction of a triangle possible in which the lengths of sides are 5 cm, 4 cm and 9 cm?

*Solution:*The lengths of the sides are 5 cm, 4 cm, 9 cm.

5 cm + 4 cm = 9 cm.

Then the sum of two smaller sides is equal to the third side. But in a triangle, the sum of any two sides should be greater than the third side.

Hence, no triangle possible with sides 5 cm, 4 cm and 9 cm.

**● ****Triangle.**Classification of Triangle.

Properties of Triangle.

Worksheet on Triangle.

To Construct a Triangle whose Three Sides are given.

To Construct a Triangle when Two of its Sides and the

included Angles are given.

To Construct a Triangle when Two of its Angles and the

included Side are given.

To Construct a Right Triangle when its Hypotenuse and One

Side are given.

Worksheet on Construction of Triangles.

5th Grade Geometry Page

5th Grade Math Problems

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