Question

Proof triangles

I know that AD is congruent with DC because of the definition of a midpoint

The line segment BD is part of both triangles. I don't know the right way to say that that side of the triangle is the same in both trI angles

Angles A and C are congruent

Is showing that two sides are the same enough to say the triangles are the same ?

Answer 1

No, two sides the same is not enough.
You need more proof.

Side, angle, side. (SAS).
AD = DC
Angle ADB = Angle CDB
BD = BD

By the SAS property, the two triangles are the same.

I think this is one way to prove it...

Or, similarly...use ASA, (Angle, side, angle).