Question

Construct an isosceles right-angled triangle ∆PQR where ∠

Answer 1

Answer:

Please find attached the required triangle drawn with Microsoft Visio

Step-by-step explanation:

The isosceles triangle ΔPQR we are to construct has the following parameters;

∠PQR = 90°

Length of side hypotenuse PR = 4 cm

Therefore, given that the triangle is right triangle is an isosceles triangle the length of each of the side legs are equal

Therefore, we have;

Length of PQ = Length of QR

The length of the legs , $\overline {PQ}$ and $\overline {QR}$, are given by Pythagoras's theorem as follows;

$\overline {PR}$ = √($\overline {PQ}$² + $\overline {QR}$²) = √($\overline {PQ}$² + $\overline {PQ}$²) = $\overline {PQ}$·√2

∴ $\overline {PQ}$ = 4 cm/(√2) = 2·√2 cm = $\overline {QR}$

The required triangle drawn with Microsoft Visio is attached