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

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

AC is common to both
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.

AFOKE88 AFOKE88 · Answer 2 · 2021-10-22T13:09:50+02:00

The next thing to know to prove that the triangles ΔABC and ΔADC are congruent by SAS theorem is that;

2 corresponding sides and the corresponding included angles of both triangles are equal.

The meaning of SAS Congruency is that;

If two sides and the included angle of one triangle are equal to the corresponding two sides and the included angle of another triangle, then the two triangles are said to be congruent by SAS postulate.

We see that the angles m∠CAD and m∠ACB are congruent as shown in the triangle. Thus;

m∠CAD ≅ m∠ACB

Since m∠CAD and m∠ACB are congruent, it means that AD and BC must be congruent.

Thus; AD ≅ BC

Now, AC is common to both triangles ΔABC and ΔADC and as such, we have 2 corresponding equal sides with the included corresponding equal angles.

Thus, the SAS Congruence postulate is proved.

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