# Common Core: High School - Geometry : Congruence

## Example Questions

### Example Question #7 : Definition Of Congruency For Triangles: Ccss.Math.Content.Hsg Co.B.7

Which theorem can be used to prove triangle congruency between triangle A and B?

AAS

AAA

SAS

ASA

SSS

SSS

Explanation:

For this particular problem there are two geometric theorems that could potentially be used to prove that the triangles are similar.

The geometric theorems that could be used:

1. Hypotenuse and One Leg of a Right Triangle (HL)

2. Side, Side, Side (SSS)

To use SSS or HL, the Pythagorean theorem will need to be used to calculate the missing side.

For these triangles the HL is the most evident to use but is not an option in the answer selections, therefore, SSS is the correct answer.

### Example Question #8 : Definition Of Congruency For Triangles: Ccss.Math.Content.Hsg Co.B.7

Identify the missing term in the statement.

The __________ geometric theorem deals with proving congruency among right triangles; specifically when the length of one leg and the length of the hypotenuse are known.

Side, Angle, Side

Angle, Angle, Side (AAS)

Hypotenuse and One Leg (HL)

Angle, Angle, Angle (AAA)

Side, Side, Side (SSS)

Hypotenuse and One Leg (HL)

Explanation:

The statement, "The __________ geometric theorem deals with proving congruency among right triangles; specifically when the length of one leg and the length of the hypotenuse are known." is describing the geometric theorem known as the Hypotenuse and One Leg theorem. When abbreviated this is seen as, HL.

Therefore, the missing term is, Hypotenuse and One Leg (HL)

### Example Question #11 : Definition Of Congruency For Triangles: Ccss.Math.Content.Hsg Co.B.7

Identify the missing term in the statement.

The __________ geometric theorem can be used to identify whether triangles that each have three known side lengths are congruent.

Side, Side, Side (SSS)

Side, Angle, Side (SAS)

Angle, Side, Angle (ASA)

Angle, Angle, Side (AAS)

Hypotenuse and One Leg (HL)

Side, Side, Side (SSS)

Explanation:

The statement, "The __________ geometric theorem can be used to identify whether triangles that each have three known side lengths are congruent." is describing the geometric theorem known as the Side, Side, Side theorem. When abbreviated this is seen as, SSS.

Therefore, the missing term is, Side, Side, Side (SSS).

### Example Question #12 : Definition Of Congruency For Triangles: Ccss.Math.Content.Hsg Co.B.7

Identify the missing term in the statement.

When two triangles have two known angles and a known side length that is in between the angles, the geometric theorem that can be used to prove congruency is known as __________

Side, Side, Side (SSS)

Angle, Angle, Angle (AAA)

Angle, Angle, Side (AAS)

Angle, Side, Angle (ASA)

Side, Angle, Side (SAS)

Angle, Side, Angle (ASA)

Explanation:

The statement, "When two triangles have two known angles and a known side length that is in between the angles, the geometric theorem that can be used to prove congruency is known as __________. " is describing the geometric theorem known as the Angle, Side, Angle theorem. When abbreviated this is seen as, ASA.

Therefore, the missing term is, Angle, Side, Angle (ASA).

### Example Question #1 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

What is the supplement of the complement of ?

Explanation:

In order to solve this problem, we need to break down each word.

We need to first find the complement of .

The complement is

Since we are given an angle of  we can substitute it for , and solve for .

Now since we need to find the supplement of the answer, we just got.

The supplement is

Now we simply substitute the answer we just got for .

### Example Question #1 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

What is the supplement of the complement of ?

Explanation:

In order to solve this problem, we need to break down each word.

We need to first find the complement of

The complement is

Since we are given an angle of  we can substitute it for , and solve for .

Now since we need to find the supplement of the answer, we just got.

The supplement is

Now we simply substitute the answer we just got for .

### Example Question #2 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

What is the supplement of the complement of ?

Explanation:

In order to solve this problem, we need to break down each word.

We need to first find the complement of .

The complement is

Since we are given an angle of  we can substitute it for , and solve for .

Now since we need to find the supplement of the answer, we just got.

The supplement is

Now we simply substitute the answer we just got for .

### Example Question #81 : High School: Geometry

What is the supplement of the complement of ?

Explanation:

In order to solve this problem, we need to break down each word.

We need to first find the complement of .

The complement is

Since we are given an angle of  we can substitute it for , and solve for.

Now since we need to find the supplement of the answer, we just got.

The supplement is

Now we simply substitute the answer we just got for .

### Example Question #4 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

What is the supplement of the complement of ?

Explanation:

In order to solve this problem, we need to break down each word.

We need to first find the complement of

The complement is

Since we are given an angle of  we can substitute it for , and solve for .

Now since we need to find the supplement of the answer, we just got.

The supplement is

Now we simply substitute the answer we just got for .

### Example Question #82 : High School: Geometry

What is the supplement of the complement of ?

Explanation:

In order to solve this problem, we need to break down each word.

We need to first find the complement of

The complement is

Since we are given an angle of  we can substitute it for , and solve for .

Now since we need to find the supplement of the answer, we just got.

The supplement is

Now we simply substitute the answer we just got for