# Common Core: High School - Geometry : Congruence

## Example Questions

### Example Question #7 : 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 #5 : 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 #6 : 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 #91 : Congruence

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 #92 : Congruence

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 Triangle Theorems: Ccss.Math.Content.Hsg Co.C.10

Are the two triangles shown congruent?

Yes

No

Yes

Explanation:

For two triangles to be congruent they must have equal corresponding angles and sides. There are five geometric theorems that can be used to prove whether triangles are congruent or not. Since, these two triangles have two defined angles and the side between the angles are defined as well, the Angle, Side, Angle geometric theorem can be used.

Looking at the triangles the corresponding angles are equal and the correspond side is also equal therefore, the triangles are congruent.

### Example Question #1 : Prove Triangle Theorems: Ccss.Math.Content.Hsg Co.C.10

Are the two triangles congruent?

No

Yes

Yes

Explanation:

For two triangles to be congruent they must have equal corresponding angles and sides. There are five geometric theorems that can be used to prove whether triangles are congruent or not. Since, these two triangles have all three sides defined, the Side, Side, Side geometric theorem can be used.

Looking at the triangles the corresponding sides are equal therefore, the triangles are congruent.

### Example Question #2 : Prove Triangle Theorems: Ccss.Math.Content.Hsg Co.C.10

Are the two triangles congruent?

Yes

No

Yes

Explanation:

For two triangles to be congruent they must have equal corresponding angles and sides. There are five geometric theorems that can be used to prove whether triangles are congruent or not. Since, these two triangles have all three sides defined, the Side, Side, Side geometric theorem can be used.

Looking at the triangles the corresponding sides are equal therefore, the triangles are congruent.

### Example Question #4 : Prove Triangle Theorems: Ccss.Math.Content.Hsg Co.C.10

Are the two triangles congruent?

No

Yes