CLASS-8
PROPERTY OF RECTANGLE
RECTANGLE –
A parallelogram is called Rectangle if one of its angles is a right angle. In the above figure, you can find, ABCD is a parallelogram in which ∠A = 90⁰. Thus ABCD is a rectangle and this is for your information, a rectangle has all the properties of a parallelogram. In addition, it has the following special properties which can separate rectangles from others to get recognize.
Property.1) All the interior angles of a rectangle are right angles.
In the figure we can observe, AB || DC => ∠A + ∠D = 180⁰, but ∠A = 90⁰, so ∠D = 90⁰
Also the opposite angles are equal. So, ∠C = ∠A = 90⁰ and ∠B = ∠D = 90⁰, so we can conclude that ∠A = ∠B = ∠C = ∠D = 90⁰.
Property.2) The diagonals of a rectangle are equal in length.
In the figure above, ∆ ABC ≅ ∆ BAD, because AB = BA,
∠ADC = ∠BAD (=90⁰) and BC = AD
So, diagonal AC = diagonal BD