Question

Abcd is a quadrilateral in which ab // dc and ad//bc prove that angle adc is eaual to angle abc

Answer 1

Given: ABCD is a quadrilateral in which AB || DC and AD || BC.

Since DC || AB,

∴ ∠CDA + ∠DAB = 180°  ......(1)  (Interior angle on the same side of the transversal AD)

Also, AD || BC,

∴ ∠DAB + ∠ABC = 180°  ......(2)

Equating equation (1) and (2),

∠CDA + ∠DAB = ∠DAB + ∠ABC

⇒ ∠CDA = ∠ABC