500
ABCD is a parallelogram and BEFC is a square. Show that triangles ABE and DCF are congruent.
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In the parallelogram ABCD, BA is congruent to CD. In the square BEFC, EB is congruent to FC. Since EB is parallel to FC and BA is parallel to CD then angles EBA and FCD are congruent. Comparing triangles ABE and DCF: angle EBA included between EB and BA in triangle ABE is congruent to angles FCD included between sides FC and CD. EB is congruent to FC and BA is congruent to CD. These two triangles are congruent. It is the SAS congruent case.