Mathematics

Problem

Consider

\triangle PQR

and

\triangle STU

in which the following measurements are given:

PQ = 5\,\text{cm},\; PR = 7\,\text{cm},\; \angle QPR = 62^{\circ}

ST = 5\,\text{cm},\; SU = 7\,\text{cm},\; \angle TSU = 62^{\circ}

a. (i) Determine whether the two triangles are congruent. Give full reasons for your answer. b. (ii) Write the correct correspondence of their vertices (for example,

\triangle PQR \cong \triangle \ldots

). c. (iii) If

QR = 4.6\,\text{cm}

, find the length of

TU

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