Page 83 - Start Up Mathematics_6

Quadrilaterals D

A four-sided polygon is called a quadrilateral. Alternatively, a quadrilateral C
is a simple closed figure formed by four line segments.
A quadrilateral has four sides and four angles. The four sides of quadrilateral B
ABCD are AB, BC, CD and DA. Its four angles are ∠A, ∠B, ∠C and ∠D. A

Adjacent Sides

Two sides are said to be adjacent, if they have a point in common. In
quadrilateral PQRS, PQ and QR, QR and RS, RS and SP, SP and PQ are S
the pairs of adjacent sides. R

Adjacent Angles

Two angles are said to be adjacent, if they have a common arm. In P Q
quadrilateral PQRS, ∠P and ∠Q, ∠Q and ∠R, ∠R and ∠S, ∠S and ∠P
are the pairs of adjacent angles.

Opposite Sides
In quadrilateral PQRS, the pair of opposite sides are PQ and RS, and SP and QR.

Opposite Angles
In quadrilateral PQRS, ∠P and ∠R, and ∠Q and ∠S are pairs of opposite angles.

Example 14: Draw a rough sketch of a quadrilateral ABCD. Draw
one of its diagonals. Which points of the diagonal
lie in the interior of the quadrilateral?
D
Solution: A diagonal is obtained by joining any two opposite
vertices. AC is one such diagonal. All points of the C
diagonal between A and C lie in the interior of the
quadrilateral.
A B
Example 15: A quadrilateral PUSH with all angles less
than 180° and a quadrilateral GATE with S
one angle greater than 180° are given. State H
in each case:
(a) One pair of opposite angles

(b) One pair of opposite sides P U
(c) One pair of adjacent angles
(d) One pair of adjacent sides T
(e) Mark two points L and M in the interior
of quadrilateral GATE such that line G

segment LM doesn’t lie wholly in its E
interior. Is it possible to have such a
line in quadrilateral PUSH? Explain.
A

75