Question

in addition to the diagram which statement is necessary to prove that the two triangles are congruent by SAS Criterion​

Answer 1

Answer:

C.

Step-by-step explanation:

SAS is set up literally...meaning that the angle HAS to be between the 2 sides in question.  Sices AB and DF are congruent, the included angles are angle ABC and DFE, so the other side to make up SAS has to be right next to the angle.  Those sides are BC and EF.  Choice C.

Answer 2

Answer:

The Answer is C

Step-by-step explanation:

SAS Property - If two sides and one common angle to these two sides are equal to the two corresponding sides and one corresponding common angle of another triangle; then both the triangles are said to be congruent.

Example: From the attached figure:

AC = DE (given)

BC = FE (given)

∠ B = ∠ F (assume 50° each)

We can observe that:

Two sides AC & BC of △ ABC are equal to corresponding sides DE & FE of △ DFE.

∠ B (common angle to sides AC & BC) of △ ABC is equal to corresponding ∠ F (common angle to sides DE & FE) of △ DFE

Therefore, from the above two observations, SAS congruence rules apply and we can say △ ABC and △ DFE are congruent.

And the corresponding relationships are as:

A ↔ D

B ↔ F

C ↔ E