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Types of Triangles on the Basis of angles

acute-angled triangle: A triangle is called an acute-angled A
triangle if all its angles are less than 90°.
56°
In the adjoining figure, DABC is an acute-angled triangle as
∠A, ∠B and ∠C are less than 90°.
67° 57°
B C
Obtuse-angled triangle: A triangle is called an obtuse-angled A
triangle if it has one obtuse angle.

In the adjoining figure, DABC is an obtuse-angled triangle since
∠ABC = 105° (obtuse). B 105° C

right-angled triangle: A triangle is called a right-angled P

triangle if it has one right angle (90°). The side opposite to the
right angle is the longest side and is called the hypotenuse. Hypotenuse

In the adjoining figure, DPQR is a right-angled triangle with 90°
∠PQR = 90°. Here, PR is the hypotenuse. Q R

Properties of sides and angles of a Triangle

1. The sum of the lengths of any two sides of a triangle is
always greater than the length of the third side.
P
In DPQR, PQ = 2 cm, QR = 4 cm and PR = 3 cm. 2 cm 3 cm

Now, PQ + QR = 2 cm + 4 cm = 6 cm, and PR = 3 cm
Clearly, PQ + QR > PR. Q 4 cm R

Check the same by taking other combinations of sides.
2. The sum of the three angles of a triangle is 180°. A

In DABC, ∠A = 60°, ∠B = 50°, ∠C = 70°. 60°

So, ∠A + ∠B + ∠C = 60° + 50° + 70° = 180°.

50° 70°
B C

Exercise 5E

A
1. Write the names of the following from the adjoining figure:
a. Vertices: _________ b. Angles: _________

c. Sides: _________
B C

120 Mathematics 5