Question

What else must you know to prove the triangles are congruent by sas?

Answer 1

Idk if this makes sense but,

You can prove it by SSS [3 sides of given triangles are congruent 

Proof: Since the given figure is parallelogram then the two opposite sides are congruent 
AB=CD & AD=BD 
and obviously the diagonal of a parallelogram are the common sides of the two triangle then they are congruent 
therefore triACD is congruent to triABC by SSS Postulate

Answer 2

Answer:

AD must be congruent to BC in order to prove the two triangles are congruent by SAS.

Step-by-step explanation:

As we have to prove the triangle congruency by SAS or Side-Angle-Side congruency, so two consecutive side along with their common angle must be congruent with the other triangle.

As in ΔABC and ΔADC already

1. AC is common to both
2. m∠CAD ≅ m∠ACB (given)

So, if AD becomes congruent to BC, then both the triangle will be congruent.

This will happen when ABCD becomes a parallelogram or rhombus or rectangle or square. Because in all of these geometric figure opposite sides are congruent.