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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