Page 139 - 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.
POLYGONS
Then, OA = OC,
OB = OD and AOB = COD = BOC = AOD = 1 right angle. Triangle 3 sides tri means 3
Quadrilateral 4 sides quad means 4
4. RECTANGLE A parallelogram in which each angle is a right Pentagon 5 sides penta means 5
angle is called a rectangle. Hexagon 6 sides hexa means 6
Heptagon 7 sides hepta means 7
In the given figure, ABCD is a rectangle in which AB || DC, Octagon 8 sides octa means 8
NonAgon 9 sides nona means 9
AD || BC and A = B = C = D = 90°. Decagon 10 sides deca means 10

PRACTICE EXERCISE 8.2
PROPERTIES OF A RECTANGLE
1. Indicate whether the following statements are true or false.
(i) Opposite sides of a rectangle are equal and parallel. a. Every square is a rectangle.
(ii) Each angle of a rectangle ts 90°• b. Every rhombus is a parallelogram.
(iii) Diagonals of a rectangle are equal.. c. Every parallelogram is a trapezium.
d. Every parallelogram is a rectangle.
Thus, in a rectangle ABCD, we have: e. Every rhombus is a square.
(i) AB = DC, AD = BC and AB || DC, AD || BC. f. Every square is a rhombus.
(ii) A = B = C = D = 1 right angle. g. A nonagon has nine sides.
(iii) Diagonal AC = diagonal BD. h. A heptagon has seven sides
i. A triangle with each angle equal to 60° is a regular polygon.
5. SQUARE A parallelogram in which all the sides are equal and each j. A quadrilateral with angles 120° , 60° , 90° and 90° is a regular polygon.
angle is a right angle, is called a square.
In the given figure, ABCD is a square in which AB = BC = CD = DA and 2. In the figure given below, AB || CD and BC = AD. What kind of quadrilateral is ABCD? If AB = 8 cm and
BC = 6 cm, what is the length of CD and AD? If A = 120° and B = 60° , write the measure of C and D.
A = B = C = D = 90°.

PROPERTIES OF A SQUARE
(i) The sides of a square are all equal.
(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: