Quadrilaterals PAWAN SINGH T.G.T(Maths) K.V. NO.2 AFS Suratgarh Presented By :- PAWAN SINGH T.G.T(Maths) K.V. NO.2 AFS Suratgarh 2nd spell inservice course

LEARNING Objective's Definition of Quadrilateral. Types of Quadrilateral. Difference between Rhombus & Square and Trapezoid &Parallelogram. Angle sum property of Quadrilateral.

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Definition:- “A Quadrilateral is polygon with four sides. And A polygon is a closed shape consisting of line segments that has at least three sides. “ OR “A flat closed shape with four straight sides is called Quadrilaterals“ A quadrilaterals has four sides, four angles and four vertices.

Each shape has four sides. Quadrilaterals “Quad” means four. Why would all of these shapes be called “quadrilaterals”? Each shape has four sides.

TYPES OF QUADRILATERALS Square A square has four sides that are each the same length. It also has four right angles (perfect corners). 1 4 3 2

Rhombus obtuse acute acute obtuse A rhombus has four sides that are each the same length. But it has two acute and two obtuse angles. obtuse acute acute obtuse

Square and Rhombus A square and a rhombus both have four sides that are the same length. So, how are they different?

Square and Rhombus a rhombus. A rhombus can be thought of as a slanted square. If we push on the left-hand side of this square, it might end up looking like… a rhombus.

The only difference between a square and a rhombus is their angles.

Trapezoid A trapezoid has four sides. Two sides are parallel. The opposing two sides are not parallel. Those are not parallel. Those are parallel.

Rectangle A rectangle has four sides – two long sides and two short sides. Two sides are parallel. The opposing two sides are also parallel. It also has four right angles.

Parallelogram A parallelogram has four sides – two long sides and two short sides. Opposite sides are parallel. But, it has two acute and two obtuse angles.

Rectangle and Parallelogram A parallelogram can be thought of as a slanted rectangle. If we push on the left-hand side of this rectangle, it might end up looking like… a parallelogram.

The only difference between a rectangle and a parallelogram is their angles.

COMPARISION OF QUADRILATERALS. Square All sides are equal & parallel Each angle 90° Rhombus 2 angles acute & 2 obtuse. Trapezoid One pair of opposite sides is parallel 2 angles acute & 2 obtuse Parallelogram Both pair of opposite sides is parallel

Special Parallelograms RHOMBUS RECTANGLE SQUARE

Angle sum Property of a Quadrilateral Let ABCD be a quadrilateral and A & C joined to get diagonal AC. We obtain two triangles ∆ ADC & ∆ ABC Using Angle sum property in ∆ADC  DAC + ACD + D = 180° ----------------- (1) Similarly, in ∆ ABC  CAB +  ACB +  A = 180° ---------------- (2) Adding (1) and (2) we get  DAC + ACD+ D + CAB + ACB + B = 180° + 180° Also, DAC + CAB = A and ACD + ACB = C SO A + B + C + D =360° The sum of the angles of a quadrilateral is 360° D c A B

Sample problem The angles of quadrilateral are in the ratio 3:5:9:13.Find all the angles of the quadrilateral. Sol‘n:-Let the angles are 3k,5k,9k&13 (multiple of k) We know Sum of angles is equal to 360° . So 3k+5k+9k+13k = 360° Or 30k = 360° Or k= 360° /30 Or k=12 Thus angle of quadrilateral are 36°,60°,108 ° & 156.°

Evaluation Quadrilateral whose two opposite sides are parallel is called …………. Trapezoid has ……. Pair of parallel sides. Polygon has ………or more sides. The sum of angles in a quadrilateral is …… If the angles of parallelogram is in ratio 1:2:1:2. Find the angles‽

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