# Common Core: High School - Geometry : Congruence

## Example Questions

### Example Question #4 : Rotation, Reflection, And Transformation Definitions: Ccss.Math.Content.Hsg Co.A.4

For an equilateral triangle that is inscribed in a circle, what is the minimum angle rotation that can be done to result in the same triangle orientation?

Possible Answers:

None of the answers.

Correct answer:

Explanation:

Recall that the circle is  degrees. It is also important to recall that an equilateral triangle is a triangle whose side lengths are equal and the angles are equal. When the triangle is inscribed in the circle three lines can be drawn from the vertex on each point to the midpoint of the opposite side. This results in the following image.

From here, calculate the central angle between two points of the triangle. Since the circle is  degrees and the triangle is divided into six equal sectors then each sector is  degrees. Now, there are two sectors between two points of the triangle. Therefore, the minimum angle rotation that can be done to result in the same triangle is  degrees.

### Example Question #5 : Rotation, Reflection, And Transformation Definitions: Ccss.Math.Content.Hsg Co.A.4

Given a circle that is divided into  equal pieces, what is the number of rotations that can occur to keep symmetry?

Possible Answers:

Correct answer:

Explanation:

To calculate the number of symmetrical rotations, take one piece and rotate it clockwise until, it results in the exact image as originally started with. Since the circle is divided into  equal pieces that means that rotating one of the pieces can be done two different times and still keep rotational symmetry, which also means keeping the angles of each piece the same and returning to the original image.

Therefore the correct answer is .

### Example Question #6 : Rotation, Reflection, And Transformation Definitions: Ccss.Math.Content.Hsg Co.A.4

Given a circle that is divided into  equal pieces, what is the number of rotations that can occur to keep symmetry?

Possible Answers:

Correct answer:

Explanation:

To calculate the number of symmetrical rotations, take one piece and rotate it clockwise until, it results in the exact image as originally started with. Since the circle is divided into  equal pieces that means that rotating one of the pieces can be done 8 different times and still keep rotational symmetry, which also means keeping the angles of each piece the same and returning to the original image.

Therefore the correct answer is .

### Example Question #7 : Rotation, Reflection, And Transformation Definitions: Ccss.Math.Content.Hsg Co.A.4

Given a circle that is divided into  equal pieces, what is the number of rotations that can occur to keep symmetry?

Possible Answers:

Correct answer:

Explanation:

To calculate the number of symmetrical rotations, take one piece and rotate it clockwise until, it results in the exact image as originally started with. Since the circle is divided into 16 equal pieces that means that rotating one of the pieces can be done  different times and still keep rotational symmetry, which also means keeping the angles of each piece the same and returning to the original image.

Therefore the correct answer is .

### Example Question #8 : Rotation, Reflection, And Transformation Definitions: Ccss.Math.Content.Hsg Co.A.4

Given a circle that is divided into  equal pieces, what is the number of rotations that can occur to keep symmetry?

Possible Answers:

Correct answer:

Explanation:

To calculate the number of symmetrical rotations, take one piece and rotate it clockwise until, it results in the exact image as originally started with. Since the circle is divided into  equal pieces that means that rotating one of the pieces can be done  different times and still keep rotational symmetry, which also means keeping the angles of each piece the same and returning to the original image.

Therefore the correct answer is .

### Example Question #9 : Rotation, Reflection, And Transformation Definitions: Ccss.Math.Content.Hsg Co.A.4

Given a circle that is divided into  equal pieces, what is the number of rotations that can occur to keep symmetry?

Possible Answers:

Correct answer:

Explanation:

To calculate the number of symmetrical rotations, take one piece and rotate it clockwise until, it results in the exact image as originally started with. Since the circle is divided into  equal pieces that means that rotating one of the pieces can be done  different times and still keep rotational symmetry, which also means keeping the angles of each piece the same and returning to the original image.

Therefore the correct answer is .

### Example Question #11 : Rotation, Reflection, And Transformation Definitions: Ccss.Math.Content.Hsg Co.A.4

Given a circle that is divided into  equal pieces, what is the number of rotations that can occur to keep symmetry?

Possible Answers:

Correct answer:

Explanation:

To calculate the number of symmetrical rotations, take one piece and rotate it clockwise until, it results in the exact image as originally started with. Since the circle is divided into  equal pieces that means that rotating one of the pieces can be done  different times and still keep rotational symmetry, which also means keeping the angles of each piece the same and returning to the original image.

Therefore the correct answer is .

### Example Question #12 : Rotation, Reflection, And Transformation Definitions: Ccss.Math.Content.Hsg Co.A.4

Given a circle that is divided into  equal pieces, what is the number of rotations that can occur to keep symmetry?

Possible Answers:

Correct answer:

Explanation:

To calculate the number of symmetrical rotations, take one piece and rotate it clockwise until, it results in the exact image as originally started with. Since the circle is divided into  equal pieces that means that rotating one of the pieces can be done  different times and still keep rotational symmetry, which also means keeping the angles of each piece the same and returning to the original image.

Therefore the correct answer is .

### Example Question #1 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

If a triangle is in quadrant three and undergoes a transformation that moves each of its coordinate points to the left three units and down one unit, what transformation has occurred?

Possible Answers:

Rotation

None of the other answers.

Extension

Translation

Reflection

Correct answer:

Translation

Explanation:

To determine the type of transformation that is occurring in this particular situation, first recall the different types of transformations.

Translation: To move an object from its original position a certain distance without changing the object in any other way.

Transformation: Refers to any of the four changes that can be done to an object geographically. Transformations include, reflections, translations, rotations, and resizing the object.

Reflection: To flip the orientation of an object over a specific line or function.

Rotation: To rotate an object either clockwise or counter clockwise around a center point.

Since each of the triangle's coordinates is moved to the left and down, it is seen that the size and shape of the triangle remains the same but its location is different. Therefore, the transformation the triangle has undergone is a translation.

### Example Question #2 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

If a rectangle has the coordinate values, , and  and after a transformation results in the coordinates , and  identify the transformation.

Possible Answers:

Non of the others

Reflection

Rotations

Dilation

Extension

Correct answer:

Reflection

Explanation:

"If a rectangle has the coordinate values, , and  and after a transformation results in the coordinates  , and  identify the transformation."

A transformation that changes the  values by multiplying them by negative one is known as a reflection across the -axis or the line

Therefore, this particular rectangle is being reflected across the -axis because the opposite of all the  values have been taken.