Question

in the given figure. if AB=CD, AD = BC then prove.angle A= angle C

Answer 1

Answer

ABCD is a quadrilateral

In which

AB=CD

AD=BC

So it is also a parallelogram

Now

Since AB is parallel to CD therefore let AD be the transversal

Angle A + Angle D =180° (co-interior angle).............(I)

Let angle A be x and angle D=180-x

Now again AD is parallel to BC let CD be the transversal

Angle D+ Angle C = 180° (co-interior angles)

180-x+ angle C =180° (from I)

Angle C=x ....(ii)

Now from I and ii

Angle A = Angle C