Question

ABCD is a trapezium in which AB || DC. IF angle A = B = 45°
Prove that:
(1) AD=BC
(1) angle C= angle CD=135​

Answer 1

Step-by-step explanation:

for given any 2 sides are parallel in trapezium the sum of deg on one side(a and d )are equal to 180deg

if a and b is 180deg

the c=d=180-45=135

Answer 2

Answer:

Given, ABCD is a trapezium in which AB || DC.

Given, angle A = B = 45°

The lines AD & BC formed with the base AB consists of equal angles at A & B

=> ABCD is an isosceles trapezium

=> AD = BC [ since AB || DC ]

Sum of adjacent angles of a trapezium = 180°

Also, Sum of interior angles of a trapezium = 360°

=> A + D = 180° and B + C = 180°

=> 45° + D = 180° and 45° + C = 180°

=> D = 180° - 45° and C = 180° - 45°

=> D = 135° and C = 135°

.•. angle C = angle D = 135°