Page 78 - Maths Class 06

A

2. Right-angled Triangle : A triangle in which one of the angles is a right angle (i e. .
90°) is called a right-angled triangle. Fig. 5.7 shows a right-angled triangle.
Y C
Right-angled triangle
Fig. 5.7
P Z

3. Obtuse-angled Triangle : A triangle in which one of the angles is
obtuse (i e. . more than 90°) is called an obtuse-angled triangle. Fig.
5.8 shows two obtuse-angled triangles. Q (a) R X (b) Y
Obtuse-angled triangles
Fig. 5.8

NOTE
The sum of all three angles of any triangle is always 180° and this is known as angle sum property of a triangle.

When the two categories mentioned above are combined, seven possible triangles are formed.

NOTE
If all angles are equal in a triangle, then all sides are also equal.
In a triangle, if all sides are equal, all angles are equal.
In a triangle, if two sides are equal, the two angles opposite to these sides are also equal.
In a triangle, if two angles are equal, the two sides opposite to these angles are also equal.

EX AM PLE 1. Name the fol low ing tri an gles in two dif fer ent ways:

13 cm
5 cm 5 cm 5 cm

12 cm
80° 80°
Fig. 5.9 (a) Fig. 5.9 (b)
SOLUTION : (a) On ba sis of sides - isos ce les tri an gles.

On basis of angles - acute-angled triangle.
(b) On basis of sides - scalene triangle.

On basis of angles - right-angled triangle.
EX AM PLE 2. Each of the two equal an gles of a tri an gle is four times the third an gle. Find all the an gles of
the tri an gle.
SOLUTION : Let the smaller angle = x

\ Other two angles = 4x and 4x
Thus, 4x + 4x + x = 180 °
9x = 180 °

78