Question

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

Answer 1

Answer:

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 $\angle C \cong\angle F$ and $CB=FE$.

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.  

Answer 2

The angle B is congruent to angle E,  2) CA=FD  3)Angle A is congruent to angle D

We solve the given problem one by one so for

!. We have to solve this problem by ASA criterion

Therefore the ASA congruence is,

What is the congruence postulate of ASA?

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.  

That is two angle and one side is congruent to the other triangle

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

That is  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.

The ASA 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.  

Look at the given triangle we can see that$\angle C$≅∠Fand CB=EF

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 .

That is  CA=FD

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.  

Two angles and one side is 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.

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.

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