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Classification Based on the Measure of Angles

Acute-angled triangle: A triangle whose all three angles are acute A
(i.e., less than 90°) is called an acute-angled triangle.
In the adjoining figure, DABC is an acute-angled triangle in which
∠A, ∠B, ∠C < 90°.
B C
Obtuse-angled triangle: A triangle whose any one angle is obtuse A
(greater than 90°) is called an obtuse-angled triangle.

In the adjoining triangle ABC, ∠B > 90° but less than 180° that is
an obtuse angle. B C

Right-angled triangle: A triangle whose any one angle is a right A
angle is called a right-angled triangle. Hypotenuse
In the adjoining figure, DABC is a right angled triangle, in which
∠B is a right angle, i.e., the measure of ∠B = 90°.
The side opposite to the right angle is called its hypotenuse. It is B C
the largest side of the right-angled triangle. A

In a right-angled triangle, if two sides are equal, then it is known 45°
as an isosceles right-angled triangle.
In the adjoining figure, DABC is an isosceles right-angled triangle 45°
as AB = BC and ∠B = 90°. B C

maths fun
How many triangles are there in the given figure?

Example 1: Write all the six elements of the following triangles and also classify each of the
triangles according to their sides and angles.
R A P P
5.2 cm 5.2 cm 4 cm 6 cm 10 cm 8 cm
(a) (b) 7 cm (c) (d)

S 5.2 cm T B 4 cm C Q 6 cm R Q 6 cm R
Solution: (a) In ΔRST,

Sides: RS = ST = RT = 5.2 cm (all sides are equal)
Vertices: R, S and T

Angles: ∠R, ∠S and ∠T (all are acute angles)
So, DRST is an equilateral and acute-angled triangle.

171 The Triangle and Its Properties