Question

ABCD is a trapezium in which AB||CD and A = B. is it an isosceles trapezium? why or why not?​

Answer 1

Answer:

Since ABCD is isosceles trapezium

So angle DAB =angle ABC =x (say)

and Angle ADC = angle DCB = y (say)

Sum of all angles of quadrilateral is 360

So x + x +y + y =360

x+y =180

Angle ADP =

2

y

and angle DAP =

2

x

(Since DP and AP are angle bisectors)

2

y

+

2

x

= 90

In triangle APD

2

y

+

2

x

+ angle DPA =180

So angle DPA = 90

So correact answer is Option C