Chapter: 8

What Are Quadrilaterals ?

Quadrilateral

A closed figure obtained by joining four non-collinear points is called a quadrilateral.

Angle Sum Property of a Quadrilateral :

Sum of all angles of a quadrilateral is 360°

Chap 8_1-01

Types Of Quadrilaterals

  • Parallelogram:

(i) Opposite sides are equal

(ii) Opposite angles are equal

(iii) Diagonals bisect each other

(iv) A pair of opposite sides is equal and parallel.

(v) Diagonals divide it into two congruent triangles.

  • Rectangle:

(i) diagonls are equal

(ii) each angle is 90°

  • Square:

(i) diagonls are equal

(ii) each angle is 90°

(iii) all sides are equal

  • Rhombus:

(i) diagonals bisect each other at right angles

(ii) all sides are equal

  • Trapezium:

(i) One pair of opposite sides is parallel

(ii) Other pair of opposite sides is non-parallel

  • Isosceles Trapezium:

(i) Two non-parallel sides are equal

(ii) one pair of opposite side is equal

  • Kite:

(i) Kite has pair of equal adjacent sides.

(ii) It is not a parallelogram

Important Points To Remember

• The diagonals of a parallelogram are equal if and only if it is a rectangle.

• If a diagonal of a parallelogram bisects one of the angles of the parallelogram then it also bisects the opposite angle.

• In a parallelogram, the bisectors of any two conssecutive angles interesect at a right angle.

• The angle bisectors of a parallelogram form a rectangle.

Mid Point Theorem

A line segment joining the mid points of any two sides of a triangle is parallel to the third side and length of the line segment is half of the parallel side.

Converse

A line through the mid point of a side of a triangle parallel to another side bisects the third side.

Intercept Theorem

If there are three parallel lines and the intercepts made by them on one transversal are equal then the intercepts on any other transversal are also equal.