Construct an isosceles triangle whose altitude is 5 cm and vertex angle is 90°.

Here, we are given with altitude of triangle, that is, 5 cm and vertex angle equals to 90°. Let us construct an isosceles triangle using the following steps of construction.

Steps of construction:

1. Draw a line segment XY using a ruler of any length.

2. Take a point M on line XY and draw a perpendicular line MP such that MP ⊥ XY; use protractor to measure angle 90°.

3. Now, with M as centre draw a circle or semicircle or an arc of radius 5 cm cutting MP at A using a compass and a ruler.

4. Construct B and C on XY such that, ∠MAB = 45° and ∠MAC = 45° . Measure the angles using a protractor.

Thus, ABC is the required triangle.