Question

ABCD is a trapezium in which AB is parallel to CD.If AD=BC,show that angleA=angleB and angleC=angleD

Answer 1

Step-by-step explanation:

Given in trapezium ABCD, AB||CD and AD = BC

Draw perpendiculars DP and CQ on AB

Consider triangles APD and BQC

∠P = ∠Q = 90°

DP = CQ [Distance between parallel sides is same]

AD = BC (Given)

Therefore, ΔAPD ≅�ΔBQC [By RHS congruence criterion]

Hence ∠A = ∠B [CPCT]