Question

Construct an isosceles right-angled triangle whose hypotenuse is of length 6 cm.

Answer 1

Let, ΔUVW be the isosceles right-angled triangle,
right-angled at U.
Hypotenuse VW = 6 cm
UV = UW
⇒ ∠UWV = ∠UVW
∠U = 90°
⇒ ∠UWV + ∠UVW = 90°
⇒ 2∠UVW = 90°
⇒ ∠UWV = ∠UVW = 45°
Steps:
1. Draw VW = 6 cm.
2. Construct ∠WVY = 45° and ∠VWX = 45°
3. Ray VY and ray WX meet at U.
Thus, UVW is the required triangle.