Examples of Properties of Triangle

We will solve some of the examples of properties of triangle.

1. In the triangle, given write the names of its three sides, three angles and three vertices.

Solution:

Three sides of ∆PQR are: PQ, QR and RP

Three angles of ∆PQR are: ∠PQR, ∠QRP and ∠RPQ

Three vertices of ∆PQR are: P, Q and R

2. Measures of two angles of a triangle are 65° and 40°. Find the measure of its third angle.

Solution:

Measures of two angles of a ∆ are 65° and 40°

Sum of the measures of two angles = 65° + 40° = 105°

Sum of all three angles of ∆ = 180°

Therefore, measure of the third angle = 180° - 105° = 75°

3. 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.