Triangle is to be drawn with the following data:

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

Problem

Triangle

PQR

is to be drawn with the following data:

PQ = 6\text{ cm}

QR = 5\text{ cm}

and

\angle PQR = 45^{\circ}

. Work out the tasks below. (a) Using ruler and compasses only, construct

\triangle PQR

with the given measurements. (b) On the opposite side of

QR

, construct another triangle

P'Q'R'

such that

Q'R' = QR

Q'P' = QP

and

\angle P'Q'R' = 45^{\circ}

. (c) Prove that

\triangle PQR \cong \triangle P'Q'R'

and state the specific congruence criterion that applies.