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.

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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