Given:
ABCD is a trapezium where
AB||CD and
AD=BC
Construction : Extends AB and draw a line through C point to DA intersecting AB produced at E
Prrof: AD||CE (from construction) &
AE||DC (AS AB||CD, & AB is extended)
AECD is a parallelogram.
In AECD, both pair of opposite sides are parallel.
∴AD=CE (opposite sides of parallelogram are equal)
But AD=BC (Given)
⇒BC=CE
So, ∠CEB=∠CBE ...(1) ( In ΔBCE, angles opposite to equal sides are equal)
For AD||CE,
& AE is the transversal,
∠A+∠CEB=180o [interior angles on same side of transversal is supplementary]
∠A=180o−∠CEB ....(2)
Also AE is line,
so, ∠B+∠CE=180o (liner pairs)
∠B+∠CBE=1800 (from (1))
∠B=180o−∠CBE ....(3)
from (2) and (3)
∠A=∠B
∴ The answer is ∠A=∠B
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