Question

2.in the following figure, show that \\( \triangle psq \cong \triangle psr \\)

3.in the given figure, \\( a p=b q, p r=q s \\). show that \\( \triangle a p s \cong \triangle b q r \\)

4.lengths of two sides of an isosceles triangle are \\( 5 \mathrm{~cm} \\) and \\( 8 \mathrm{~cm} \\), find the perimeter of the triangle.
5.write the rule of congruence in the following pairs of congruent triangles

Explanation:

Step1: Determine the possible cases for the isosceles triangle

An isosceles triangle has two equal sides. So, there are two cases:

• Case 1: The equal sides are \(5\) cm. Then the sides of the triangle are \(5\) cm, \(5\) cm, and \(8\) cm.
• Case 2: The equal sides are \(8\) cm. Then the sides of the triangle are \(8\) cm, \(8\) cm, and \(5\) cm.

Step2: Calculate the perimeter for each case

• For Case 1:

The perimeter \(P_1=5 + 5+8\)
\(P_1 = 18\) cm.

• For Case 2:

The perimeter \(P_2=8 + 8+5\)
\(P_2=21\) cm.

Answer:

The perimeters of the isosceles triangle are \(18\) cm and \(21\) cm.