Question

Construct an isosceles right-angled triangle ∆PQR where ∠

Answer 1

Please find attached the required triangle drawn with Microsoft Visio

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