• If A, B, C, D are four points in a plane such that no three of them are collinear and the line segments AB, BC, CD and DA do not intersect except at their end points, the figure formed by these four segments is called a quadrilateral.
• ∠A, ∠B, ∠C, ∠D are four angles of quad.
• Two line segments AC and BD are called the diagonals of quad. ABCD also we have the following four consecutive sides. The sides of a quad. which have one vertex in common are called consecutive sides. These are called as adjacent sides. For example, in the quad. ABCD: AB & BC; BC & CD; CD & DA; DA & AB are four pairs of the consecutive sides.
Sides of a quad. which do not have a common vertex are called opposite sides. For example, in the quad. ABCD; AB and DC form a pair of opposite sides. BC and AD form another pair of opposite sides.
Two angles of a quad, are consecutive angles if they have a common arm. In the fig.
∠A and ∠B
∠B and ∠C
∠C and ∠D
∠D and ∠A are four pairs of the consecutive angles of quad. ABCD.
Opposite angles: Angles of a quad. which have no side in common are called opposite angles. For example, in the above quad.
∠A and ∠C;
∠B and ∠D are two pairs of opposite angles.
Remember: 1.The sum of the angles of a quad. is 360°.
2. If the sides of a quadrilateral are produced, the sum of the four exterior angles so formed is 360°.
Types of Quadrilateral
1. A quad. having exactly one pair of parallel sides is called a trapezium.
2. A quad. in which both pairs of opposite sides are parallel is called a parallelogram.
3. A parallelogram having all sides equal is called a rhombus .
4. A parallelogram whose each angle in a right angle is called a rectangle.
5. A parallelogram having all sides equal and each angle equal to a right angle is called a square
6. A quad. having two pairs of equal adjacent sides but unequal opposite side is called a Kite.
Note: A quad. is a parallelogram if
(i) its opposite sides are equal
(ii) its opposite angles are equal
(iii) its diagonals bisect each other
(iv) it has one pair of opposite sides equal and parallel.
7. The diagonals of a rhombus bisect each other at right angles.
• The diagonals of rectangle are equal.
Diagonal BD = Diagonal AC
• The diagonals of a square are equal and bisect each other at right angles.
• The line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of it.
∴ EF = ½ BC
• 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.