Quadrilaterals

QuadrilateralQuadrilateral

What is What is quadrilateral?quadrilateral? A A  quadrilaterquadrilater

alal    is a four- is a four-sided polygon sided polygon with four with four angles. angles.

There are There are many kinds many kinds of of quadrilateraquadrilateralsls ..

Kinds of Kinds of QuadrilateralQuadrilateral ParallelogramParallelogram RectangleRectangle SquareSquare RhombusRhombus KiteKite TrapeziumTrapezium

Properties of Properties of kinds of kinds of quadrilateralquadrilateral

ParallelograParallelogramm

Meaning – A Meaning – A quadrilateral with each quadrilateral with each pair of opposite sides pair of opposite sides parallel.parallel.

PropertiesProperties1.1. Opposite sides are equal.Opposite sides are equal.2.2. Opposite angles are Opposite angles are

equal.equal.3.3. Diagonals bisect one Diagonals bisect one

another.another.4.4. Each diagonal of a Each diagonal of a

parallelogram separates parallelogram separates it into two congruent it into two congruent triangles. triangles.

RectanglRectanglee

Meaning ~ A Meaning ~ A parallelogram with a parallelogram with a right angle.right angle.

PropertiesProperties1.1. Opposite sides are equal.Opposite sides are equal.2.2. Opposite angles are Opposite angles are

equal.equal.3.3. Diagonals bisect one Diagonals bisect one

another.another.4.4. Each of the angle is a Each of the angle is a

right angle.right angle.5.5. Diagonals are equal.Diagonals are equal.

SquareSquare

Meaning ~ A rectangle Meaning ~ A rectangle with sides of equal with sides of equal length.length.

PropertiesProperties1.1. Opposite sides are equal. Opposite sides are equal.

2.2. Opposite angles are Opposite angles are

equal.equal.3.3. Diagonals bisect one Diagonals bisect one

another.another.4.4. Diagonals are Diagonals are

perpendicular to each perpendicular to each other.other.

5.5. Each of the angle is a Each of the angle is a right angle.right angle.

6.6. Diagonals are equal.Diagonals are equal.

RhombusRhombus

Meaning ~ A Meaning ~ A parallelogram with sides parallelogram with sides of equal length.of equal length.

PropertiesProperties1.1. Opposite sides are equal.Opposite sides are equal.2.2. Opposite angles are Opposite angles are

equal.equal.3.3. Diagonals bisect one Diagonals bisect one

another.another.4.4. Diagonals are Diagonals are

perpendicular to each perpendicular to each other.other.

Kite Kite

Meaning ~ A quadrilateral Meaning ~ A quadrilateral with exactly two pairs of with exactly two pairs of equal consecutive sides.equal consecutive sides.

PropertiesProperties1.1. The diagonals are The diagonals are

perpendicular to one perpendicular to one another.another.

2.2. One of the diagonals One of the diagonals bisects the other.bisects the other.

3.3. In the figure mLB = mLD In the figure mLB = mLD but mLA is not equal to but mLA is not equal to mLCmLC

TrapeziuTrapeziumm

Meaning ~Meaning ~ A A quadrilateral with one quadrilateral with one pair of parallel sides.pair of parallel sides.

Properties Properties 1.1. The diagonals of are The diagonals of are

equal in length. equal in length.

Mid-Point Mid-Point TheoremTheoremThe segment The segment

joining the joining the midpoints of two midpoints of two sides of a triangle sides of a triangle is parallel to the is parallel to the third side and half third side and half of it.of it.

Prove Prove AM=BM [midpoint].AM=BM [midpoint].

< AMP = <MBQ < AMP = <MBQ [Corresponding angles for [Corresponding angles for parallel lines cut by an parallel lines cut by an transversal].transversal].

<BQM=<QCP=<APM <BQM=<QCP=<APM [Corresponding angles for [Corresponding angles for parallel lines cut by an parallel lines cut by an transversal].transversal].

<BMQ=<MAP [When 2 <BMQ=<MAP [When 2 pairs of corresponding pairs of corresponding angles are congruent in a angles are congruent in a triangle, the third pair is triangle, the third pair is also congruent.]also congruent.]

AMP is congruent to AMP is congruent to MBQ. [ASA]MBQ. [ASA]

Therefore: AP=MQ=PC Therefore: AP=MQ=PC and MP=BQ=QC. and MP=BQ=QC. 

By: Shefali KumarBy: Shefali KumarClass: IX-BClass: IX-BSchool: Ramagya School: Ramagya School, Sector-50, School, Sector-50, NoidaNoidaRoll No.: 29Roll No.: 29