Page 124 - classs 6 a_Neat

PROPERTIES OF A RHOMBUS
(i) AB = BC = CD = DA.
(i) The opposite sides of a rhombus are parallel. (ii) A = B =C = D = 90°.
(ii) All the sides of a rhombus are equal. (iii) Diagonal AC = diagonal BD
(iii) The opposite angles of a rhombus are equal.
(iv) The diagonals of a rhombus bisect each other at right angles. 6. KITE A quadrilateral which has two pairs of equal adjacent sides
but unequal opposite sides, ts called a kite.
Thus, in a rhombus ABCD, we have:
(i) AB || DC and AD || BC. In the given figure ABCD is a kite
(ii) AB = BC = CD = DA. in which CB = CD and AB = AD
(iii) DAB = BCD and ABC = CDA. but AD ≠ BC and AB ≠ CD.
(iv) Let the diagonals AC and BD intersect at 0.

Then, OA = OC, PRACTICE EXERCISE 7.3
OB = OD and AOB = COD = BOC = AOD = 1 right angle.
1.Name the sides, vertices and angles of the given quadrilaterals
4. RECTANGLE A parallelogram in which each angle is a right
angle is called a rectangle.

In the given figure, ABCD is a rectangle in which AB || DC,

AD || BC and A = B = C = D = 90°.

PROPERTIES OF A RECTANGLE

(i) Opposite sides of a rectangle are equal and parallel.
(ii) Each angle of a rectangle ts 90°•
(iii) Diagonals of a rectangle are equal..

Thus, in a rectangle ABCD, we have:
(i) AB = DC, AD = BC and AB || DC, AD || BC.
(ii) A = B = C = D = 1 right angle.
(iii) Diagonal AC = diagonal BD. Draw a quadrilateral. Name it AXYB. Draw its diagonals and name them.

5. SQUARE A parallelogram in which all the sides are equal and each 3. In the given figure, list the points that lie
angle is a right angle, is called a square. a. in the interior of the quadrilateral PQRS.
In the given figure, ABCD is a square in which AB = BC = CD = DA and b. in the exterior of the quadrilateral PQRS.
c. on the boundary of the quadrilateral PQRS.
A = B = C = D = 90°.

4. Three angles of a quadrilateral measure 120° , 60° and 100° , respectively.
PROPERTIES OF A SQUARE Find the measure of the fourth angle.
(i) The sides of a square are all equal. 5. Draw two quadrilaterals to show the difference between a convex and a concave quadrilateral.
(ii) Each angle of a square ts go0•
(iii) The diagonals of a square are equal and bisect each other
at right angles.

Thus, in a square ABCD, we have: