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**UNDERSTANDING QUADRILATERALS BY:SHIVANI, VIII**

K.V A.F.S BIDAR BANGLORE REGION UNDERSTANDING QUADRILATERALS BY:SHIVANI, VIII

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INTRODUCTION The surface which is flat and plane is known as plane surface . For example paper . A curve in the plane whose starting point is also the end point and which has no other self-intersections . A simple closed curve is also known as Jordan curve

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POLYGON Simple closed curve made up of line segments is called polygon. CURVES THAT ARE POLYGONS Example 1 CURVES THAT ARE NOT POLYGONS Example 2

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**CLASSIFICATION OF POLYGON**

Number of sides or vertices Classification Sample of figure 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon

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DIAGONALS A diagonal is a line segment connecting two non – consecutive vertices of a polygon.

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**CONCAVE AND CONVEX POLYGON**

The polygon , in which all the diagonals lie in interior is known as convex polygon. The polygon , in which some diagonals lie in exterior is known as concave polygon.

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**ANGLE SUM PROPERTY The angle sum property of quadrilateral is 360. C B**

The angle sum property of triangle is 180 . We have divided a quadrilateral into two triangles .So, =360

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**KINDS OF QUADRILATERALS**

Based on the nature of the sides or angles of a quadrilateral, it gets special names.

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**PARALLELOGRAM A quadrilateral with each pair of opposite**

PROPERTIES A quadrilateral with each pair of opposite side parallel. Opposite sides are equal Opposite angles are equal. Diagonals bisect each other. Adjacent angles are supplementary.

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**SQAURE All the sides are equal. All the angles are equal.**

PROPERTIES All the sides are equal. All the angles are equal. The diagonals bisect each other. Also a rectangle.

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**RECTANGLE The opposite sides are equal. Diagonals are equal.**

PROPERTIES The opposite sides are equal. Diagonals are equal. Each of the angle is right angle. A parallelogram with a right angle.

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**RHOMBUS of equal length. 2. All the properties of parallelogram.**

1. A parallelogram with sides of equal length. 2. All the properties of parallelogram. 3. Diagonals are perpendicular to each other.

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**KITE PROPERTIES A A quadrilateral with exactly**

two pairs of equal consec- B D utive sides. The diagonals are perpendic- ular to each other C One of the diagonal bisect the other. In the figure m B=m D but m A= m C

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**TRAPEZIUM Trapezium is a quadrilateral with a pair of parallel sides**

PROPERTIES Trapezium is a quadrilateral with a pair of parallel sides (NOTE: The arrow marks indicate parallel lines)

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THE END

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Math 310 9.2 Polygons.

Math 310 9.2 Polygons.

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