Understanding Quadrilaterals Class 8

Mathematics class 8

1. quadrilaterals UNDERSTANDING

2. Made By : Jai Hans Class : 8 – F Roll Number : 28

3. curves A plane curve is a curve that lies in a single plane or a plane surface like paper. A plane curve may be closed or open .

4. POLYGONS Polygon is a closed plane figure bounded by three or more straight sides that meet in pairs in the same number of vertices, and do not intersect other than at these vertices.

5. Parts of a polygon The endpoints of the sides of polygons are called vertices. When naming a polygon, its vertices are named in consecutive order either clockwise or counterclockwise. Consecutive sides are two sides that have an endpoint in common. The four-sided polygon in Figure below could have been named ABCD, BCDA, or ADCB, for example. It does not matter with which letter you begin as long as the vertices are named consecutively. Sides AB and BC are examples of consecutive sides. There are four pairs of consecutive sides in this polygon.

6. Parts of a polygon A diagonal of a polygon is any segment that joins two nonconsecutive vertices. Figure shows five-sided polygon QRSTU. Segments QS , SU , UR , RT and QT are the diagonals in this polygon. Diagonals of a polygon can be found with the formula given below :

7. CLASSIFICATION of Polygons Polygons first fit into two general categories— convex and concave. A polygon is concave if there are two points somewhere inside it for which a segment with these as its endpoints cuts at least 2 of the sides of the polygon. A polygon that is not concave is called convex.

8. CLASSIFICATION of Polygons

9. CLASSIFICATION of Polygons Polygons are also classified by how many sides (or angles or vertices) they have. The following lists the different types of polygons and the number of sides that they have: A triangle is a three-sided polygon A quadrilateral is a four-sided polygon. A pentagon is a five-sided polygon. A hexagon is a six-sided polygon. A septagon or heptagon is a seven-sided polygon. An octagon is an eight-sided polygon. A nonagon is a nine-sided polygon. A decagon is a ten-sided polygon

10. Regular Polygons When a polygon is both equilateral and equiangular, it is referred to as a regular polygon. For a polygon to be regular, it must also be convex. .

11. Sum of interior angles of polygon Sum of the interior angles of a polygon = (N - 2) x 180° Note : Sum of exterior angles of any polygon is always 360 degrees & the sum of interior angles of a polygon can be more or less than 360 degrees which can be calculated by the formula given above.

12. A Quadrilateral is any shape with 4 sides . The word “quadrilateral” comes from two Latin words “ quadri ” which means ‘a variant of four’ and “lateral” which means side. PROPERTIES: with four sides with four angles with four vertices With one pair of diagonals Quadrilaterals

13. Interior Angle Sum Property: According to this property, the sum of the interior angles of the quadrilateral is 360° Exterior Angle Sum Property: According to this property, the sum of the exterior angles of the quadrilateral is 360° Quadrilaterals

14. Quadrilaterals Rectangle Parallelogram Rhombus Square Isosceles Trapezoid Kite Quadrilateral (Trapezium) Trapezoid

15. Types of Quadrilaterals RECTANGLE Opposite sides are  parallel  and  congruent  . The diagonals  bisect  each other. The diagonals are  congruent . A  rectangle  is a four-sided shape where every angle is a  right angle  (90°).

16. RHOMBUS A  rhombus  is a four-sided shape where all sides have equal length. Also opposite sides are parallel   and   opposite angles are equal. Another interesting thing is that the diagonals (dashed lines in second figure) of a rhombus bisect each other at right angles.

17. SQUARE A  square  has equal sides and every angle is a right angle (90°) A square can be thought of as a special case of other quadrilaterals, for example: a  rectangle  but with adjacent sides equal a  parallelogram  but with adjacent sides equal and the angles all 90° a  rhombus  but with angles all 90°

18. PARALLELOGRAM A parallelogram is a  quadrilateral  with opposite sides  parallel . Also opposite angles are equal (angles "a“ is same as angles "b“ ). The opposite sides are equal .The adjacent angles are supplementary and the diagonals bisects each other ; but they are not equal. It is the "parent" of some other quadrilaterals, which are obtained by adding restrictions of various kinds: A  rectangle  is a parallelogram but with all four interior angles fixed at 90°. A  rhombus  is a parallelogram but with all sides equal in length. A  square  is a parallelogram but with all sides equal in length and all angles fixed at 90°.

19. TRAPEZIUM Trapezoid Isosceles Trapezoid A  trapezium is quadrilateral  which has at least one pair of parallel sides . It is called an Isosceles trapezium if the sides that aren't parallel are equal in length and both angles coming from a parallel side are equal Note : Trapezium is UK terminology & in US terminology it is called as Trapezoid.

20. KITE Two pairs of adjacent sides of a kite are equal in length. One pair of opposite  angles  (the ones that are between the sides of unequal length) are equal in size. One diagonal bisects the other. Diagonals intersect at  right angles . A kite is a  quadrilateral  whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other. Kite quadrilaterals are named for the wind-blown, flying  kites , which often have this shape 

21. QUADRILATERALS

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