Question
Construct an isosceles right$-$angled triangle whose hypotenuse is of length $6 \ cm.$
✓
Answer
Let, $\triangle UVW$ be the isosceles right$-$angled triangle,
right$-$angled at $U.$
Hypotenuse $VW = 6 \ cm$
$UV = UW$
$\Rightarrow \angle UWV = \angle UVW$
$\angle U = 90^\circ $
$\Rightarrow \angle UWV + \angle UVW = 90^\circ $
$\Rightarrow 2\angle UVW = 90^\circ $
$\Rightarrow \angle UWV = \angle UVW = 45^\circ $
Steps:
$1.$ Draw $VW = 6 \ cm.$
$2.$ Construct $\angle WVY = 45^\circ $ and $\angle VWX = 45^\circ $
$3.$ Ray $VY$ and ray $WX$ meet at $U.$
Thus, $\text{UVW}$ is the required triangle.
right$-$angled at $U.$
Hypotenuse $VW = 6 \ cm$
$UV = UW$
$\Rightarrow \angle UWV = \angle UVW$
$\angle U = 90^\circ $
$\Rightarrow \angle UWV + \angle UVW = 90^\circ $
$\Rightarrow 2\angle UVW = 90^\circ $
$\Rightarrow \angle UWV = \angle UVW = 45^\circ $
Steps:
$1.$ Draw $VW = 6 \ cm.$
$2.$ Construct $\angle WVY = 45^\circ $ and $\angle VWX = 45^\circ $
$3.$ Ray $VY$ and ray $WX$ meet at $U.$
Thus, $\text{UVW}$ is the required triangle.
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