If two quadrilaterals $ABCD$ and $PQRS$ have angles $A$, $B$, $C$, $D$ equal to angles $P$, $Q$, $R$, $S$ respectively and $AB=PQ$, $DC=SR$, and if $AD$ is not parallel to $BC$, prove that the quadrilaterals are congruent.

What I have done - Given all angles are equal, we have to prove that $BC=QR$ and $AD=PS$. I have tried using congruency of triangles as follows: $AB=PQ$, and $\angle A$ is equal to $\angle P$. However, I cannot find the third equation to complete the proof.

Can someone please help?


hint: first you need to prove PS is not parallel to QR.

then make AE//BC, PT//QR, prove AE=PT, AC=PR, then ....

enter image description here


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.