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1. 1. Raksha Sharma
2. 2.  Square: Quadrilateral with four equal sides and four right angles (90 degrees) Indicates equal sides Box indicates 900 angle
3. 3. Types of Quadrilaterals  Rectangle: Quadrilateral with two pairs of equal sides and four right angles (90 degrees) Indicates equal sides Box indicates 900 angle
4. 4. Types of Quadrilaterals  Parallelogram: Quadrilateral with opposite sides that are parallel and of equal length and opposite angles are equal Indicates equal sides
5. 5. Types of Quadrilaterals  Rhombus: Parallelogram with four equal sides and opposite angles equal Indicates equal sides
6. 6. Types of Quadrilaterals  Trapezoid: Quadrilateral with one pair of parallel sides Parallel sides never meet.
7. 7. Types of Quadrilaterals  Irregular shapes: Quadrilateral with no equal sides and no equal angles
8. 8. Name the Quadrilaterals 1 2 3 4 5 6 rectangle irregular rhombus parallelogram trapezoid square
9. 9. Interior Angles  Interior angles: An interior angle (or internal angle) is an angle formed by two sides of a simple polygon that share an endpoint  Interior angles of a quadrilateral always equal 360 degrees
10. 10. A diagonal of a parallelogram divides it into two congruent triangles. In a parallelogram ,opposite sides are equal. If each pair of opposite sides of quadrilateral is equal then it is a parallelogram. In a parallelogram opposite angles are equal. If in a quadrilateral each pair of opposite angles is equal then it is a parallelogram. The diagonals of a parallelogram bisect each other. If the diagonals of a quadrilateral bisect each other then it is a parallelogram.
11. 11. We have studied many properties of a parallelogram in this chapter and we have also verified that if in a quadrilateral any one of those properties is satisfied, then it becomes a parallelogram. There is yet another condition for a quadrilateral to be a parallelogram. It is stated as follows: A QUDRILATERAL IS A PARALLELOGRAM IF A PAIR OF OPPOSITE SIDES IS EQUAL AND PARALLEL.
12. 12. A Q C P B D S R Example: ABCD is a parallelogram in which P and Q are mid points of opposite sidesAB and CD. If AQ intersects DP at S and BQ intersects CP at R, show that: 1. APCQ is a parallelogram 2. DPBQ is a parallelogram 3. PSQR is a parallelogram SOLUTION: 1. In quadrilateral APCQ, AP is parallel to QC AP = ½ AB , CQ = ½ CD , AB = CD, AP = CQ Therefore APCQ is a parallelogram. (theorem 8.8) 2.Similarly quadrilateral DPBQ is a parallelogram because DQ is parallel to PB and DQ = PB 3. In quadrilateral PSQR SP is parallel to QR and SQ is parallel to PR. SO ,PSQR is a parallelogram.
13. 13. What is the sum of angles in triangle ADC? D C BA We know that angle DAC+ angle ACD+ angle D = 180 Similarly in triangleABC, angle CAB + angle ACB + angle B = 180 Adding 1 and 2 we get , angles DAC + ACD + D + CAB + ACB + B =180 + 180 = 360 Also, angles DAC + CAB = angle A and angle ACD + angle ACB = angle C So, angle A + angle D +angle B + angle C = 360 i.e.THE SUM OFTHE ANGLES OF A QUADRILATERAL IS 360.