Question

The condition_______?proves that ∆ABC and ∆EFG are congruent by the SAS criterion.

Answer 1

Answer:

(1)  D.Angle C is congruent to to Angle F. (2) C. SSS. (3) C. cannot be congruent to.

Step-by-step explanation:

1)

From the given figure it is noticed that

$AC=EG$

$CB=GF$

According to SAS postulate,  if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then both triangles are congruent.

The included angles of congruent sides are angle C and angle G.

So, condition "Angle C is congruent to to Angle F"  will prove that the ∆ABC and ∆EFG are congruent by the SAS criterion.

2)

If $AB\neq EF$

According to SSS postulate,  if all three sides in one triangle are congruent to the corresponding sides in the other.

Since two corresponding sides are congruent but third sides of triangles are not congruent, therefore SSS criterion for congruence is violated.

3)

Since two corresponding sides are congruent but third sides of triangles are not congruent, therefore the included angle of congruent sides are different.

$\angle C\neq \angle G$

Therefore angle C and angle F cannot be congruent to each other.