RAYAT SHIKSHAN SANSTHAS NANDRE VIDYALAYA NANDRE SUBJECT GEOMETRY

RAYAT SHIKSHAN SANSTHA’S NANDRE VIDYALAYA NANDRE

SUBJECT -GEOMETRY STD – 9 Th

SUPERVISOR

GEOMETRY Standard Ix 5. QUADRILATERALS

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

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

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

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

TYPES OF QUADRILATERAL PARALLELOGRAM RECTANGLE SQUARE RHOMBUS TRAPEZIUM ISOSCELES TRAPEZIUM KITE

PARALLELOGRAM PROPERTIES OF A PARALLELOGRAMØ OPPOSITE SIDES OF A PARALLELOGRAM ARE PARALLEL. Ø OPPOSITE SIDES ARE CONGRUENT. Ø OPPOSITE ANGLES ARE CONGRUENT. Ø DIAGONALS OF A PARALLELOGRAM BISECT EACH OTHER.

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 EVERY RECTANGLE IS A PARALLELOGRAM. PROPERTIES OF A RECTANGLEØ ALL THE PROPERTIES OF PARALLELOGRAM HOLDS GOOD FOR RECTANGLE. Ø FURTHER, EACH ANGLE IS A RIGHT ANGLE. Ø DIAGONALS OF A RECTANGE ARE CONGRUENT. Sub: -Geometry

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

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

TEST OF RHOMBUS • If diagonals of a quadrilateral bisect each other at right angle, then quadrilateral is a rhombus.

SQUARE Properties of a squareØ All the sides and angles of a square congruent. Ø All the angles are right angles. Ø Diagonals of a square congruent & perpendicular bisectors of each other.

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

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

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

S P A Q B R PROPERTIES OF A TRAPEZIUMØ LINE SEGMENT JOINING MID-POINTS OF NONPARALLEL SIDES IS 1) PARALLEL TO ITS PARALLEL SIDES 2) HALF THE SUM OF THE LENGTHS OF ITS PARALLEL SIDES

ISOSCELES TRAPEZIUM Properties of a isosceles trapeziumØ This is a special type of trapezium. Ø Non parallel sides are congruent. Ø Further, all properties of trapezium holds good in this case.

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