Two right-angled triangular wooden panels

MATHEMATICS · Subjective · GCSE · Mathematics · Geometry and Measures · Geometry and Measures

Problem

Two right-angled triangular wooden panels,

\triangle ABC

and

\triangle PQR

, are prepared so that

\angle B = \angle Q = 90^{\circ}

. It is known that

AC = PR = 13\text{ cm}

and

AB = PQ = 5\text{ cm}

. (i) Prove that the two panels are congruent. (ii) Calculate the lengths

BC

and

QR

. (iii) Explain how one panel can be placed over the other so that they coincide exactly.