Two triangles and are such that , ,

MATHEMATICS · Multi-part · CBSE · Mathematics · Triangles · Triangles

Problem

Two triangles

\triangle ABC

and

\triangle PQR

are such that

\angle B = 90^\circ

\angle Q = 90^\circ

AB = PQ = 6\,\text{cm}

AC = PR = 10\,\text{cm}

and

BC = 8\,\text{cm}

. (i) Prove that

\triangle ABC \cong \triangle PQR

. (ii) Hence find the length of

QR

. (iii) If

\angle C = 40^\circ

, find

\angle R

. State the reason for your answer.