Quadrilaterals G-5

QUADRILATERALS : 

- DR. MRS. JAYSHREE ATRE QUADRILATERALS

INTRODUCTION : 

INTRODUCTION WORD QUADRILATERAL IS DERIVED FROM TWO WORDS “QUADRI” MEANS “FOUR” AND “LATERAL” MEANS “SIDES”.

PROPERTIES OF A QUADRILATERAL : 

PROPERTIES OF A QUADRILATERAL P Q NO THREE POINTS ARE COLLINEAR. R S COMMON POINT OF ANY OF THE TWO SEGMENTS PQ, QR, RS, ST IS AN END POINT ONLY. CONTD….

CONTD…. : 

CONTD…. 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. P R Q S INTERIOR OF THE QUADRILATERAL IS A CONVEX SET BUT QUADRILATERAL IS NOT A CONVEX SET. THE SUM OF THE MEASURES OF ALL ANGLES OF A QUADRILATERAL IS 360 DEGREES.

TYPES OF QUADRILATERAL : 

TYPES OF QUADRILATERAL

PARALLELOGRAM : 

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.

TESTS OF PARALLELOGRAM : 

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.

RECTANGLE : 

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.

TEST OF RECTANGLE : 

TEST OF RECTANGLE IF DIAGONALS OF A PARALLELOGRAM ARE CONGRUENT, THEN IT IS A RECTANGLE.

RHOMBUS : 

RHOMBUS PROPERTIES OF A RHOMBUS- ALL THE SIDES OF A RHOMBUS ARE CONGRUENT. DIAGONALS OF A RHOMBUS ARE PERPENDICULAR BISECTORS OF EACH OTHER.

TEST OF RHOMBUS : 

TEST OF RHOMBUS IF DIAGONALS OF A QUADRILATERAL BISECT EACH OTHER AT RIGHT ANGLE, THEN QUADRILATERAL IS A RHOMBUS.

SQUARE : 

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. CONTD…

CONTD… : 

CONTD… 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.

TEST OF SQUARE : 

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

TRAPEZIUM : 

TRAPEZIUM PROPERTIES OF A TRAPEZIUM- TRAPEZIUM IS A QUADRILATERAL ONLY ONE PAIR OF OPPOSITE SIDES IS PARALLEL. CONTD…

CONTD… : 

CONTD… 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

ISOSCELES TRAPEZIUM : 

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. CONTD…

CONTD… : 

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

KITE : 

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

INTERCEPT MADE BY THREE PARALLEL LINES THEOREMS : 

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. I D F E G C B A l m n t2 t1

MID - POINT THEOREM : 

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. R A Q C P B

Slide 22: 

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