Prove: It is easy to prove with what is known.

△ODC is all equal to△△ OAB (SAS)

So ∠C=∠A

So DC//AB (internal dislocation angles are equal and two straight lines are parallel)

2. In △ABC, AB=AC, point D is the midpoint of BC, and point E is on AD. Find the triangles in the diagram and explain why they are congruent.

Triangle ABD≌ triangle ACD

Because point D is the midpoint of BC, BD=CD.

And because AB=AC and AD are common sides, according to SSS, two triangles are congruent.

Triangle ABE?/ triangle ACE

Because point e is on the center line of triangle ABC,

So BE=CE

And because AB=AC, AE is the common side, according to SSS, two triangles are congruent.

Triangle EBD≌ triangle ECD

Because BD=CD BE=CE ED is the same side, according to SSS, two triangles are congruent.