Question

In a quadrilateral PQRS

(i) Name the sides, angles, vertices and diagonals.
(ii) Also name all the pairs of adjacent sides, adjacent angles, opposite sides and opposite angles.

Answer 1

Hint: In order to solve the problem use the figure and simple visualization. Basic definitions of quadrilateral will be used to solve the second part of the problem.

Complete step-by-step answer:
For the quadrilateral PQRS
Sides: $PQ,QR,RS,SP$
Angles: $\mathrm{\angle }PQR,\mathrm{\angle }QRS,\mathrm{\angle }RSP,\mathrm{\angle }SPQ$
Vertices: $P,Q,R,S$
Diagonal: $PR,QS$

Pairs of adjacent sides:
$\left\{PQ,QR\right\},\left\{QR,RS\right\},\left\{RS,SP\right\},\left\{SP,PQ\right\}$
Pairs of adjacent angles:
$\left\{\mathrm{\angle }PQR,\mathrm{\angle }QRS\right\},\left\{\mathrm{\angle }QRS,\mathrm{\angle }RSP\right\},\left\{\mathrm{\angle }RSP,\mathrm{\angle }SPQ\right\},\left\{\mathrm{\angle }SPQ,\mathrm{\angle }PQR\right\}$
Pairs of opposite sides:
$PS,QR\text{ and }QP,RS$
Pairs of opposite angles
$\mathrm{\angle }QRS,\mathrm{\angle }SPQ\text{ and }\mathrm{\angle }RSP\mathrm{\angle }PQR$

Note: A quadrilateral is a polygon with four edges and four vertices or corners. Adjacent sides are sides of a polygon that have a common vertex. Two angles are Adjacent when they have a common side and a common vertex (corner point) and don't overlap.