1. Std:-9th Sub:-Geometry Quadrilateral
Rayat shikshan sanstheche, Sau Ksturabai Shripati Kadam Vidyalaya,Indapur.
Std:-9th
Sub:-Geometry
Quadrilateral

2. Kite Trapezium Parallelogram Rhombus Rectangle Square Quadrilateral
2 pairs of equal adjacent sides
1 pair of // opp. Sides
Kite
Trapezium
Sum of interior angles is 1800
One of the diagionals is axis of symmetry
Parallelogram
2 diagionals are 
2 pairs of opp.// sides
4 equal sides
Rhombus
Properties of trapesium
2 pairs of opposite sides are equal.(opp. sides of // gram)
2 pairs of opposite angles are equal (opp. s of // gram)
Diagonals bisect each other (diag. Of // gram)
Properties of // gram and kite
Diagonals bisects each interior angle
4 right angles
Rectangle
4 right angles and 4 equal sides
450
Properties of // gram
Properties of rhombus/rectangle
Diagonals are equal
Angles between each diagional and each side is 450
Square

3. Trapeziums Definition : 1 pair of parallel sides Properties:
Sum of interior angles is 1800

4. Parallelogram Definition : 2 pairs of opp. parallel sides Properties:
2 pairs of opposite sides are equal. (opp. sides of // gram)
Diagonals bisect each other
(diag. Of // gram)
2 pairs of opposite angles are equal (opp. s of // gram)

5. Conditions for Parallelogram
If 1 pair of opposite sides is equal and parallel then the quadrilateral is parallelogram
(opp. sides eq. and //)
If 2 pairs of opposite sides are equal then the quadrilateral is parallelogram. (opp. sides eq.)
If diagonals bisect each other then the quadrilateral is parallelogram
(diag. Bisect each other)
If 2 pairs of opposite angles are equal then
the quadrilateral is parallelogram. (opp. s of eq.)

6. Rhombus Definition : a // gram or a kite of 4 equal sides Properties:
2 pairs of opposite sides are equal. (opp. sides of // gram)
Diagonals bisect each other
(diag. Of // gram)
Diagonals bisects each interior angle
2 pairs of opposite angles are equal (opp. s of // gram)
Diagonals are 

7. Rectangle Definition : a parallelogram of 4 right angles Properties:
2 pairs of opposite sides are equal. (opp. sides of // gram)
Diagonals are equal
Diagonals bisect each other
(diag. Of // gram)
2 pairs of opposite angles are equal (opp. s of // gram)

8. Square
Definition : a // gram of 4 right angles and 4 equal sides
Properties:
2 pairs of opposite sides are equal. (opp. sides of // gram)
Diagonals are equal
2 pairs of opposite angles are equal (opp. s of // gram)
Diagonals bisect each other
(diag. Of // gram)
Diagonals are 
450
Angles between each diagonal and each side is 450

9. Example 3: In the figure, ABCD is a parallelogram. Find x and y.
680 x 2y
AD//BC (Given)
x+680=1800 (prop. Of trapezium)
 x=1120 (1500-y)+2y=1800 (prop. Of trapezium) y=1800
 y= =300

10. Example 4: In the figure, ABCD is a parallelogram. Find x and y.
DAB=DCB (opp. s of // gram)
x+200=3x-100
2x=300 x=150 DAB+CBA=1800 (int.s , AD//BC)
x+200+y=1800
y=1800 y=1450

11. INTERCEPT THEOREM X Y
transversal B P
intercept A D C Q

12. INTERCEPT THEOREM A B C D E F
If AB//CD//EF then
(intercept theorem)

13. MID-POINT THEOREM A N M B C
IF AM = MB and AN =NC then (a) MN // BC (b) MN =
(Abbreviation: Mid-point theorem)