Page 190 - ICSE Math 6

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5. In DABC given alongside, E is the mid-point of BC and
AD is the altitude. Is BD = DC? Which among AB, AE,
AD and AC is the shortest?

Quadrilateral B E D C

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

Parts of a quadrilateral
Adjacent sides

Two sides are said to be adjacent, if they have a point in common. In quadrilateral
PQRS given alongside, all the pairs of adjacent sides are: (i) PQ and QR, (ii) S
QR and RS, (iii) RS and SP, and (iv) SP and PQ. R
Adjacent angles

Two angles are said to be adjacent, if they have a common arm. In quadrilateral
PQRS given alongside, all the pairs of adjacent angles are: (i) ∠P and ∠Q, P Q
(ii) ∠Q and ∠R, (iii) ∠R and ∠S, and (iv) ∠S and ∠P.
Opposite sides

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

Opposite angles
In the same quadrilateral PQRS, ∠P and ∠R, and ∠Q and ∠S are the pairs of opposite angles.
D C
Diagonal
A line segment joining any two non-consecutive vertices is called a diagonal.
In quadrilateral ABCD given alongside, AC and BD are the diagonals.

Interior and exterior A B
S R
In the adjoining figure, the shaded area is the interior of the quadrilateral
PQRS and the area outside the quadrilateral is the exterior of the quadrilateral.

Types of quadrilaterals
P Q
• Parallelogram: A parallelogram is a quadrilateral in which
both pairs of opposite sides are parallel.

• Rectangle: A rectangle is a parallelogram in which each
angle is a right angle.

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