Question

In Fig.9.21, AB || DC & AB = DC.
Q. Is ∆ABC is congruent to ∆CDA by SAS Congruence Condition? If yes, explain why?

Answer 1

Yes, ∆ABC is congruent to ∆CDA.
AB = DC (opposite sides of a parallelogram are equal)
AC = CA (both are same)
angle A = angle B (interior alternate angles are equal)

Therefore, ∆ABC congruent to ∆CDA by S.A.S.

AB and DC are sides.(S)
A and B are angles.(A)
AC and CA are sides.(S)

Answer 2

Proof- Yes This proof goes under proof of SAS congruence.
In triangle ABC & CDA
AB=CD(given)
AC=AC(common)
Angle CAD=AngleACD(Alternative angle)
So ABC triangle= CDA triangle(SAS Rule)