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1. Raksha Sharma

2.  Square: Quadrilateral with four equal sides
and four right angles
(90 degrees)
Indicates equal sides
Box indicates 900 angle

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. Types of Quadrilaterals
 Parallelogram: Quadrilateral with opposite
sides that are parallel and of equal length and
opposite angles are equal
Indicates equal sides

5. Types of Quadrilaterals
 Rhombus: Parallelogram with four equal
sides and opposite angles equal
Indicates equal sides

6. Types of Quadrilaterals
 Trapezoid: Quadrilateral with one pair of
parallel sides
Parallel sides never meet.

7. Types of Quadrilaterals
 Irregular shapes: Quadrilateral with no equal
sides and no equal angles

8. Name the Quadrilaterals
1
2 3
4 5 6
rectangle irregular rhombus
parallelogram trapezoid square

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. 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. 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. 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. 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.