The that ∆abc and ∆efg are congruent by the sas criterion.

if ab ≠ ef, the for congruency is violated. in this situation, angle c g.

1a). a. angle a is congruent to angle e
2a.) b. angle b is congruent to to angle f
3a.) c. ab=ef
4d.) d. angle congruent to angle g

2a). a. ssa
2b.) b. asa
2b.) c. sss
2b) d. sas

3a). a. may be congruent to
3b). b. is congruent to
3c). c. cannot be congruent to

(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

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

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.

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

The condition angle C is congruent to angle G proves that ∆ABC and ∆EFG are congruent by the SAS criterion.

If AB ≠ EF, the SSS criterion for congruency is violated. In this situation, angle C cannot be congruent to angle G.

Step-by-step explanation:

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