Question

Abcd is a trapezium in which ab is parallel to cd.If ad =bc. Show that angle a = angle b

Answer 1

Given - ABCD is a trapezium. AB||CD . AD=BC(a pair of side of trapezium is equal and one pair is parrellel)
TO Prove - angle A=Angle B

By Construction - draw CE || AD

In Quadrilateral- AECD,
AD||CE(By const.)
AE||CD
AS, both the pair of opposite sides is equal,so AECD is a ||gm
AD = EC (opposite sides of a llgm)
and, AD=BC
SO, EC=BC
∠EBC =∠BEC (angles opposite to equal
sides) - (i)

Now :-
∠ABC+ ∠EBC = 180° (L·P)
USING (i) -> ∠ABC +∠BEC = 180° - (ii)
∠BAD+∠BEC = 180° (co-interior angels) - (iii)


Comparing (ii) and (iii)
∠ABC+∠BEC =∠BAD+∠BEC

SO ,∠BAD =∠ABC
∴, ∠A =∠B

Hence Proved