Mathematics

Problem

Triangles

\triangle PQR

and

\triangle STU

are right-angled at

Q

and

T

respectively. The following measurements are known:

PQ = ST = 5\,\text{cm}

PR = SU = 13\,\text{cm}

QR = 12\,\text{cm}

. a. (i) Prove that

\triangle PQR \cong \triangle STU

. b. (ii) Write the congruence criterion you have used. c. (iii) Find the length

TU