Question

In parallelogram ABCD, one way to prove that diagonals and bisect each other is to prove triangle AXB congruent to triangle CXD. Which triangle congruency theorem proves that the triangles are congruent?

https://gordon.owschools.com/media/o_anageo_ccss_2014/2/img_geou04l20_12.gif

A. Angle Side Angle (ASA)
B. Side Side Side (SSS)
C. Side Angle Side (SAS)
D. Angle Angle Side (AAS)

Answer 1

Hints:
Based on the definition of a parallelogram is "A quadrilateral with both pairs of opposite sides parallel."
(ref. http://www.mathopenref.com/parallelogram.html)
you can show
\(\angle ABD \cong \angle CDB\)
\(\angle BAC \cong \angle DCA\)
and finally
\(mAB \cong mDC\) (takes a few steps).
Try the above steps, and if they work, choose your answer.

Note that if you use a different definition of a parallelogram, the result can be different.