Inspiration Swami Ramanand Vidyalaya Jr College Ramanandnagar Teacher

Inspiration

Swami Ramanand Vidyalaya & Jr. College Ramanandnagar Teacher Name : - Miss. Lakule J. P.

Sub – Mathematics th Std – 8

Unit – Quadrilaterals

Sub Units Types of quadrilaterals 1. Parallelogram 2. Rhombus

1. Parallelogram. Definition : - A quadrilateral with opposite sides parallel is called parallelogram Diagram Properties of the quadrilateral 1. The opposite sides of a parallelogram are congruent. 2. The opposite angles of a parallelogram are congruent. 3. The diagonal of a parallelogram bisect each other.

Parallelogram PQRS is shown in the fig. S P O Q R In the figure along side shows parallelogram PQRS (1) If L(PO) = 5. 2 cm, L(PR) = ? Solution : L(PR) = 2 x L(PO) (Diagonals of a parallelogram bisect each other. ) (2) If m ∠Q = 510 then m∠S = ? m∠R = ? m ∠Q = m ∠S (Opposite angles of a parallelogram are congruent) ∴ m ∠S = 510 but m ∠P + m ∠Q + m ∠R + m ∠S = 3600 m ∠P + 51 + m ∠ R + 51 = 360 m ∠P + m ∠R = 360 – 102 = 258 But m ∠ P = m ∠R ∴ m ∠R + m ∠R = 258 ∴ 2 m ∠R = 258 ∴ m ∠R = 1290

Example 1. In parallelogram PQRS m ∠Q= 1300 find the measures of other angles of PQRS 2. The measures of opposite angle of a parallelogram are (3 x-2)0 and (50 -x)0 find the measure of each angle of the parallelogram.

Rhombus Definition : - A quadrilateral with all four sides congruent is called a rhombus = =

Properties of the Rhombus : 1)The diagonals of a rhombus are bisect each other at right angles 2)Each diagonal of a rhombus is the perpendicular bisector of other. 3)The opposite angles of a rhombus are congruent.

Example: 1) If the length of one side of a rhombus is 7. 5 cm, find the lengths of the remaining sides. Solution : - All the sides of a rhombus are congruent. The length of one side of a rhombus is given to be 7. 5 cm. Ans. The length of each of the remaining sides of the rhombus is 7. 5 cm. 2) The diagonals seg XZ and seg YW of rhombus XYZW intersect each other in the point P. if L(XP) = 8 cm. Find length XZ. Solution : - The diagonals of a rhombus bisect each other the point P is the point of intersection of the diagonals X ∴ P is the midpoint of diagonal XZ Y ∴ L(XZ) = 2 L(XP) = 2 x 8 cm. = 16 cm. P Ans : - L(XZ) = 16 cm. Z

Solve the Following examples. 1 The diagonals AC and BD of a rhombus ABCD intersects at point O. Find m ∠AOD and m ∠BOC. 2. In the rhombus KING, m ∠K = 700 and m ∠I = 1100. Find the measures of the others angles of the rhombus KING.