Diagonal is drawn in quadrilateral

MATHEMATICS · Subjective · CBSE · Mathematics · Triangles · Triangles

Problem

Diagonal

PR

is drawn in quadrilateral

PQRS

. It is given that

\angle QPR = \angle SRP

\angle QRP = \angle SPR

and

PQ = RS

. (i) Prove that

\triangle PQR \cong \triangle RSP

. (ii) Deduce the relation between

PQ

and

RS

, and between the lines

PQ

and

RS

. (iii) Using the result of (ii), prove that

PQRS

is a parallelogram. (iv) If

PQ = RS = 6.5\,\text{cm}

and

QR = 4\,\text{cm}

, determine the perimeter of the parallelogram.