# Common Core: High School - Geometry : Congruence

## Example Questions

### Example Question #3 : Prove Triangle Theorems: Ccss.Math.Content.Hsg Co.C.10

Are the two triangles shown congruent?

No

Yes

No

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 not equal and the correspond side is also not equal therefore, the triangles are not congruent.

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

Are the two triangles congruent?

No

Yes

No

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 not equal therefore, the triangles are not congruent.

### Example Question #5 : Prove Triangle Theorems: Ccss.Math.Content.Hsg Co.C.10

Are the two triangles shown congruent?

Yes

No

No

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 not equal therefore, the triangles are not congruent.

### Example Question #5 : Prove Triangle Theorems: Ccss.Math.Content.Hsg Co.C.10

Are the two triangles shown congruent?

No

Yes

No

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 not equal and the correspond side is also not equal therefore, the triangles are not congruent.

### Example Question #101 : Congruence

Are the two triangles congruent?

No

Yes

No

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 not equal therefore, the triangles are not congruent.

### Example Question #105 : Congruence

Are these 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 two defined sides and one angle is also defined, the Side, Side, Angle geometric theorem can be used.

Looking at the triangles the corresponding angle are equal and the correspond sides are also equal therefore, the triangles are congruent.

### Example Question #101 : Congruence

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 two defined angles and the side defined as well, the Angle, Angle, Side 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 #102 : Congruence

Are the two triangles shown congruent?

No

Yes

No

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 not equal therefore, the triangles are not congruent.

### Example Question #101 : High School: Geometry

What is known if  is said to be a parallelogram?

Opposite side lengths are parallel.

All of the other answers are correct.

All of the other answers are correct.

Explanation:

A parallelogram is a special type of quadrilateral meaning, it is a shape that has four sides with opposite sides being parallel.

Drawing the parallelogram  can be done as follows.

Looking at the image it can be said that,

and .

Therefore, all of the possible answer choices are correct.

### Example Question #1 : Prove Parallelogram Theorems: Ccss.Math.Content.Hsg Co.C.11

Which of the following helps prove an image is a parallelogram?

Two Lines must be Perpendicular

One Set of Parallel Lines

Congruent Opposite Angles

Angles that Exceed