1. UNIT : Quadrilaterals
Standard : Ix
Patil Sandip Navanath.

2. Introduction.
Terms related to quadrilaterals
Properties of quadrilateral
Properties of a particular quadrilateral
1. Parallelogram
2. Rectangle
3. Rhombus
4. Square
5. Trapezium
6. Isosceles Trapezium
Mid-point theorem&Converse

3. INTRODUCTION
WORD QUADRILATERAL IS DERIVED FROM TWO WORDS “QUADRI” MEANS “FOUR” AND “LATERAL” MEANS “SIDES”.
M.S.V.SATARA.

4. PROPERTIES OF A QUADRILATERAL
NO THREE POINTS ARE COLLINEAR. Q
COMMON POINT OF ANY OF THE TWO SEGMENTS PQ, QR, RS, ST IS AN END POINT ONLY. Q R
IF A LINE CONTAINING ANY ONE OF THE FOUR SEGMENTS PQ, QR, RS, QS IS DRAWN, THEN REMAINING TWO POINTS LIE ON THE SAME SIDE OF THIS LINE.
INTERIOR OF THE QUADRILATERAL IS A CONVEX SET BUT QUADRILATERAL IS NOT A CONVEX SET.
M.S.V.SATARA.

5. Terms related to quadrilaterals
Elements
Names of the elements
Vertices
Point A,
Sides
segAK,
Angles
AKJ,
Diagonals
seg
Pairs of adjacent / consecutive angles
Pairs of opposite sides
Pairs of adjacent sides K A I J
M.S.V.SATARA.

6. TYPES OF QUADRILATERAL
PARALLELOGRAM
RECTANGLE
RHOMBUS
SQUARE
TRAPEZIUM
ISOSCELES TRAPEZIUM
KITE
M.S.V.SATARA.

7. PARALLELOGRAM PROPERTIES OF A PARALLELOGRAM-
OPPOSITE SIDES OF A PARALLELOGRAM ARE PARALLEL.
OPPOSITE SIDES ARE CONGRUENT.
OPPOSITE ANGLES ARE CONGRUENT.
DIAGONALS OF A PARALLELOGRAM BISECT EACH OTHER.
M.S.V.SATARA.

8. TESTS OF PARALLELOGRAM
If opposite sides of quadrilateral are congruent, then quadrilateral is parallelogram.
If opposite angles of quadrilateral are congruent, then quadrilateral is parallelogram.
If diagonals of a quadrilateral bisect each other, then quadrilateral is a parallelogram.
M.S.V.SATARA.

9. RECTANGLE EVERY RECTANGLE IS A PARALLELOGRAM.
PROPERTIES OF A RECTANGLE-
ALL THE PROPERTIES OF PARALLELOGRAM HOLDS GOOD FOR RECTANGLE.
FURTHER, EACH ANGLE IS A RIGHT ANGLE.
DIAGONALS OF A RECTANGE ARE CONGRUENT.
M.S.V.SATARA.

10. TEST OF RECTANGLE
IF DIAGONALS OF A PARALLELOGRAM ARE CONGRUENT, THEN IT IS A RECTANGLE.
M.S.V.SATARA.

11. RHOMBUS PROPERTIES OF A RHOMBUS-
ALL THE SIDES OF A RHOMBUS ARE CONGRUENT.
DIAGONALS OF A RHOMBUS ARE PERPENDICULAR BISECTORS OF EACH OTHER.
M.S.V.SATARA.

12. TEST OF RHOMBUS
If diagonals of a quadrilateral bisect each other at right angle, then quadrilateral is a rhombus.
M.S.V.SATARA.

13. SQUARE Properties of a square-
All the sides and angles of a square are congruent.
All the angles are right angles.
Diagonals of a square are congruent & perpendicular bisectors of each other.
M.S.V.SATARA.

14. A parallelogram having congruent adjacent sides and one angle right, is a square.
Rectangle with congruent adjacent sides is a square.
Rhombus with one right angle is a square.

15. TEST OF SQUARE
IF DIAGONALS OF A QUADRILATERAL ARE CONGRUENT AND BISECT EACH OTHER AT RIGHT ANGLE, THEN QUADRILATERAL IS A SQUARE.
M.S.V.SATARA.

16. TRAPEZIUM PROPERTIES OF A TRAPEZIUM- TRAPEZIUM IS A QUADRILATERAL
ONLY ONE PAIR OF OPPOSITE SIDES IS PARALLEL.
CONTD…
M.S.V.SATARA.

17. PROPERTIES OF A TRAPEZIUM- B R Q
PROPERTIES OF A TRAPEZIUM-
LINE SEGMENT JOINING MID-POINTS OF NON-PARALLEL SIDES IS
1) PARALLEL TO ITS PARALLEL SIDES
2) HALF THE SUM OF THE LENGTHS OF ITS PARALLEL SIDES
M.S.V.SATARA.
M.S.V.SATARA.

18. ISOSCELES TRAPEZIUM Properties of a isosceles trapezium-
This is a special type of trapezium.
Non parallel sides are congruent.
Further, all properties of trapezium holds good in this case.
M.S.V.SATARA.

19. DIAGONALS OF A ISOSCELES TRAPEZIUM ARE CONGRUENT.B B A D D D C C C M N
DIAGONALS OF A ISOSCELES TRAPEZIUM ARE CONGRUENT.

20. KITE PROPERTIES OF A KITE- Seg AB Seg AD Seg BC Seg DC Seg BM Seg MD
DIAGONAL AC IS PERPENDICULAR BISECTOR OF BD.
KITE A B D M A C
M.S.V.SATARA.

21. INTERCEPT MADE BY THREE PARALLEL LINES THEOREMS
1. IF THREE PARALLEL LINES MAKE CONGRUENT INTERCEPTS ON A TRANSVERSAL THEN THEY MAKE CONGRUENT INTERCEPTS ON ANY OTHER TRANSVERSAL. t2 t1 l G D A m E B n C F I
M.S.V.SATARA.

22. Mid - point theorem
In a triangle, the line segment joining the mid points of any two sides is parallel to third side and is half of it. A Q R P B C
M.S.V.SATARA.