Select the correct answer from each drop-down menu. 1. if , then ∆abc and ∆def are congruent by the asa criterion. a.) ab=de b.)ca=fd c.)angle b is congruent to angle e d.)angle a is congruent to angle d 2. if , then ∆abc and ∆def are congruent by the sas criterion. a.) ab=de b.)ca=fd c.)angle b is congruent to angle e d.)angle a is congruent to angle d 3. ∆abc and ∆def are congruent if a.) angle a is congruent to angle d b.) ab=de c.) ab=df

1. C) Angle B is congruent to angle E.

2. B) CA=FD

3. A) Angle A is congruent to angle D.

Step-by-step explanation:

Let us see our given problems one by one.

1. ASA congruence postulate states that when two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then two triangles are congruent.  

Upon looking at our diagram we can see that angle C and Side CB of ∆ABC is congruent to angle F and side FE of ∆DEF respectively.  

In order these two triangles be congruent by ASA angle B must be equal to angle E as CB is included side of ∆ABC between angles C and B and FE is included side of ∆DEF between angles F and E.

Therefore, option C is the correct choice.

2. SAS congruence postulate states that when two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then two triangles are congruent.  

Upon looking at our triangles we can see that and .

In order triangles ABC and DEF be congruent by SAS criterion side CA must be equal to side FD as angle C is included angle between sides CB and CA of ∆ABC and angle F is included angle between sides FD and FE of ∆DEF.

Therefore, option B is the correct choice.  

3. AAS postulate of congruence states that when two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then two triangles are congruent.  

We can see that side CB of ∆ABC in non included side between angles A and C. Side FE of ∆DEF is non included side between angles D and F.

Upon looking at our given options we can see that ∆ABC and ∆DEF will be congruent by AAS postulate of congruence, if angle A is congruent to angle D.

Therefore, option A is the correct choice.