Page 177 - ICSE Math 7

On the basis of angles
A
Acute-angled triangle 60°
A triangle in which all the three angles are acute (less than 90°) is known
as an acute-angled triangle.

80° 40°
B C
Obtuse-angled triangle A
A triangle in which one of the angles is obtuse (greater than 90°) is known 45°
as an obtuse-angled triangle.

100° 35°
Right-angled triangle B C

A triangle in which one angle is right angle (90°) is known as a right-angled A
triangle. In a right-angled triangle, the side opposite to the right angle is known 60°
as the hypotenuse of the triangle. Hypotenuse
If two sides of a right-angled triangle are equal, then it is known as an isosceles
right-angled triangle. As hypotenuse is the longest side, it can never be equal B 30° 90° C
to any of the other two sides.

Properties of Triangles

Property 1: The sum of all the three angles of a triangle is 180°. P A Q
Consider a DABC. From vertex A, draw a line PQ parallel to BC. Extend
side BC of DABC to form line RS. So, PQ || RS and AB is a transversal.
Therefore, ∠ABC = ∠PAB (Alternate angles)
Similarly, PQ || RS and AC is a transversal. R B C S
Therefore, ∠ACB = ∠QAC (Alternate angles)
Now, ∠PAB + ∠BAC + ∠QAC = 180° (Straight angle)
⇒ ∠ABC + ∠BAC + ∠ACB = 180°

⇒ ∠B + ∠A + ∠C = 180°
Thus, the sum of all the three angles of a triangle is 180°.
Property 2: If two sides of a triangle are equal, then the angles opposite to them are also equal.
Conversely, if two angles of a triangle are equal, then the sides opposite to them are also equal.

Points to remember A

• As two sides of an isosceles triangle are equal, the angles opposite to them
are also equal. In the adjoining figure, DABC is an isosceles triangle with
AB = AC. Hence, ∠ABC = ∠ACB. B C

• As the two sides are equal of an isosceles right-angled triangle, the angles A
opposite to them are also equal. 45°
Hence, ∠ABC = ∠CAB = 45°.

45°
B C

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