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.
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.
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?
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.