Transformation and Congruence of Rigid Motions: CCSS.Math.Content.HSG-CO.B.6 - Geometry

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Question

Jenny has drawn a rectangle in the upper left hand corner of a piece of paper. If she folds the paper in half and traces the rectangle on the other half of the paper, what type of rigid motion has occurred?

Answer

This situation describes a real life application of geometry where the coordinate grid can be seen as the piece of paper. Since Jenny is tracing the rectangle after the paper is folded it can be seen that the fold is an axis and the new rectangle is congruent to the original one. Therefore, the rigid motion describing this situation is a reflection.

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Question

Which of the following is NOT a rigid motion?

Answer

Recall that a rigid motion is that that preserves the distances while undergoing a motion in the plane. This is also called an isometry, rigid transformations, or congruence transformations and there are four different types.

These basic type of rigid motions include the following:

Rotation

Reflection

Translation

Glide Reflection

Therefore, of the answer selections, "Expansion" is the term that is NOT a rigid motion.

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Question

Jill and Jane sit next to each other in math class. Jill has a sheet of paper and Jane asks her for half of it to take notes on because she left her notebook in the locker. If Jill cuts the sheet of paper in half, has a rigid motion occurred?

Answer

Recall that a rigid motion is that that preserves the distances between points within the object while undergoing a motion in the plane. This is also called an isometry, rigid transformations, or congruence transformations and there are four different types. The piece of paper is the object in this situation. Since the paper is cut in half, it does not preserve the shape of the object and thus, is not a rigid motion.

Therefore, the answer is "No".

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Question

Jane and Bob are filling up water balloons for a party they are throwing. Jane thinks the balloons should have more water in them so she fills them fuller. Each water balloon's circumference is one inch greater than before. Does this describe a rigid motion?

Answer

Recall that a rigid motion is that that preserves the distances between points within the object while undergoing a motion in the plane. This is also called an isometry, rigid transformations, or congruence transformations and there are four different types. The water balloons are the objects in this situation. Since the they are filled with more water to increase their circumferences, it does not preserve the shape of the object and thus, is not a rigid motion.

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Question

Select the answer that best completes the following definition:

A motion that preserves distance in the plane is called a __________.

Answer

A rigid motion is that that preserves the distances while undergoing a motion in the plane. This is also called an isometry, rigid transformations, or congruence transformations and there are four different types.

These basic type of rigid motions include the following:

Rotation

Reflection

Translation

Glide Reflection

Therefore, "A motion that preserves distance in the plane is called a rigid motion".

Compare your answer with the correct one above

Question

Determine whether the statement is true or false.

For a translation to be considered rigid, the starting and ending figures must be congruent.

Answer

Recall that a rigid motion is that that preserves the distances while undergoing a motion in the plane. This is also called an isometry, rigid transformations, or congruence transformations and there are four different types. Therefore, for the translation to be considered "rigid" the two figures must be congruent by definition of a rigid motion.

Therefore, the statement, "For a translation to be considered rigid, the starting and ending figures must be congruent." is true.

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Question

$\bigtriangleup ABC$ has a rigid motion applied to it that results in $\bigtriangleup A'B'C'$ . What can be concluded about the relationship between these two triangles.

Answer

A rigid motion is that that preserves the distances while undergoing a motion in the plane. This is also called an isometry, rigid transformations, or congruence transformations and there are four different types.

Regardless of which type of rigid motion occurred, the following is true about the triangles' angles:

$\\measuredangle A\cong\measuredangle A' \\measuredangle B\cong\measuredangle B' \\measuredangle C\cong\measuredangle C'$

The following is also true about the side lengths:

$\\overline{AB}\cong \overline{A'B'} \\overline{BC}\cong \overline{B'C'} \\overline{CA}\cong \overline{C'A'}$

Therefore, of the answer choices $\measuredangle A\cong \measuredangle A'$ is the correct choice.

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Question

$\bigtriangleup ABC$ has a rigid motion applied to it that results in $\bigtriangleup A'B'C'$ . What can be concluded about the relationship between these two triangles.

Answer

A rigid motion is that that preserves the distances while undergoing a motion in the plane. This is also called an isometry, rigid transformations, or congruence transformations and there are four different types.

Regardless of which type of rigid motion occurred, the following is true about the triangles' angles:

$\\measuredangle A\cong\measuredangle A' \\measuredangle B\cong\measuredangle B' \\measuredangle C\cong\measuredangle C'$

The following is also true about the side lengths:

$\\overline{AB}\cong \overline{A'B'} \\overline{BC}\cong \overline{B'C'} \\overline{CA}\cong \overline{C'A'}$

Therefore, of the answer choices $\overline{AB}\cong \overline{A'B'}$ is the correct choice.

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Question

Determine whether the statement is true or false:

A glide reflection is a synonym for a rigid motion translation.

Answer

A glide reflection is a rigid motion that occurs when a figure is translated a certain distance and then reflected or reflected and then translated.

A translation is a rigid motion describing when a object is moved a certain distance.

A glide reflection contains a translation but it is not a synonym for translation therefore, the statement is false.

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Question

Determine whether the statement is true or false:

All glide reflections are reflections.

Answer

A glide reflection is a rigid motion that occurs when a figure is translated a certain distance and then reflected or reflected and then translated. In either case, a glide reflection aways contains a reflection.

Therefore, the statement, "All glide reflections are reflections." is true.

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Question

Sally has a quarter that is face up on the desk. If she slides it to Bob on the other side of the desk and he flips it over so that the tails side is facing up, is it a rigid motion?

Answer

In the situation where Sally has a quarter that is face up on the desk. The coin is the object. Then she slides it to Bob on the other side of the desk and he flips it over so that the tails side is facing up. Therefore, since the coin maintains it shape it is undergoing a translation to reach the other side of the desk and a reflection to flip the coin. This describes a glide reflection which is in fact, a rigid motion.

Therefore, the statement is describing a rigid motion. The answer is "Yes"

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Question

Sally has a quarter that is face up on the desk. Then she slides the coin to Bob on the other side of the desk and he flips it over so that the tails side is facing up. What type of rigid motion does this situation describe?

Answer

In the situation where Sally has a quarter that is face up on the desk. The coin is the object. Then she slides it to Bob on the other side of the desk and he flips it over so that the tails side is facing up. Therefore, since the coin maintains it shape it is undergoing a translation to reach the other side of the desk and a reflection to flip the coin. This describes a glide reflection which is in fact, a rigid motion.

Compare your answer with the correct one above

Question

Jenny has drawn a rectangle in the upper left hand corner of a piece of paper. If she folds the paper in half and traces the rectangle on the other half of the paper, what type of rigid motion has occurred?

Answer

This situation describes a real life application of geometry where the coordinate grid can be seen as the piece of paper. Since Jenny is tracing the rectangle after the paper is folded it can be seen that the fold is an axis and the new rectangle is congruent to the original one. Therefore, the rigid motion describing this situation is a reflection.

Compare your answer with the correct one above

Question

Which of the following is NOT a rigid motion?

Answer

Recall that a rigid motion is that that preserves the distances while undergoing a motion in the plane. This is also called an isometry, rigid transformations, or congruence transformations and there are four different types.

These basic type of rigid motions include the following:

Rotation

Reflection

Translation

Glide Reflection

Therefore, of the answer selections, "Expansion" is the term that is NOT a rigid motion.

Compare your answer with the correct one above

Question

Jill and Jane sit next to each other in math class. Jill has a sheet of paper and Jane asks her for half of it to take notes on because she left her notebook in the locker. If Jill cuts the sheet of paper in half, has a rigid motion occurred?

Answer

Recall that a rigid motion is that that preserves the distances between points within the object while undergoing a motion in the plane. This is also called an isometry, rigid transformations, or congruence transformations and there are four different types. The piece of paper is the object in this situation. Since the paper is cut in half, it does not preserve the shape of the object and thus, is not a rigid motion.

Therefore, the answer is "No".

Compare your answer with the correct one above

Question

Jane and Bob are filling up water balloons for a party they are throwing. Jane thinks the balloons should have more water in them so she fills them fuller. Each water balloon's circumference is one inch greater than before. Does this describe a rigid motion?

Answer

Recall that a rigid motion is that that preserves the distances between points within the object while undergoing a motion in the plane. This is also called an isometry, rigid transformations, or congruence transformations and there are four different types. The water balloons are the objects in this situation. Since the they are filled with more water to increase their circumferences, it does not preserve the shape of the object and thus, is not a rigid motion.

Compare your answer with the correct one above

Question

Select the answer that best completes the following definition:

A motion that preserves distance in the plane is called a __________.

Answer

A rigid motion is that that preserves the distances while undergoing a motion in the plane. This is also called an isometry, rigid transformations, or congruence transformations and there are four different types.

These basic type of rigid motions include the following:

Rotation

Reflection

Translation

Glide Reflection

Therefore, "A motion that preserves distance in the plane is called a rigid motion".

Compare your answer with the correct one above

Question

Determine whether the statement is true or false.

For a translation to be considered rigid, the starting and ending figures must be congruent.

Answer

Recall that a rigid motion is that that preserves the distances while undergoing a motion in the plane. This is also called an isometry, rigid transformations, or congruence transformations and there are four different types. Therefore, for the translation to be considered "rigid" the two figures must be congruent by definition of a rigid motion.

Therefore, the statement, "For a translation to be considered rigid, the starting and ending figures must be congruent." is true.

Compare your answer with the correct one above

Question

$\bigtriangleup ABC$ has a rigid motion applied to it that results in $\bigtriangleup A'B'C'$ . What can be concluded about the relationship between these two triangles.

Answer

A rigid motion is that that preserves the distances while undergoing a motion in the plane. This is also called an isometry, rigid transformations, or congruence transformations and there are four different types.

Regardless of which type of rigid motion occurred, the following is true about the triangles' angles:

$\\measuredangle A\cong\measuredangle A' \\measuredangle B\cong\measuredangle B' \\measuredangle C\cong\measuredangle C'$

The following is also true about the side lengths:

$\\overline{AB}\cong \overline{A'B'} \\overline{BC}\cong \overline{B'C'} \\overline{CA}\cong \overline{C'A'}$

Therefore, of the answer choices $\measuredangle A\cong \measuredangle A'$ is the correct choice.

Compare your answer with the correct one above

Question

$\bigtriangleup ABC$ has a rigid motion applied to it that results in $\bigtriangleup A'B'C'$ . What can be concluded about the relationship between these two triangles.

Answer

A rigid motion is that that preserves the distances while undergoing a motion in the plane. This is also called an isometry, rigid transformations, or congruence transformations and there are four different types.

Regardless of which type of rigid motion occurred, the following is true about the triangles' angles:

$\\measuredangle A\cong\measuredangle A' \\measuredangle B\cong\measuredangle B' \\measuredangle C\cong\measuredangle C'$

The following is also true about the side lengths:

$\\overline{AB}\cong \overline{A'B'} \\overline{BC}\cong \overline{B'C'} \\overline{CA}\cong \overline{C'A'}$

Therefore, of the answer choices $\overline{AB}\cong \overline{A'B'}$ is the correct choice.

Compare your answer with the correct one above

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Transformation and Congruence of Rigid Motions: CCSS.Math.Content.HSG-CO.B.6 - Geometry

Jenny has drawn a rectangle in the upper left hand corner of a piece of paper. If she folds the paper in half and traces the rectangle on the other half of the paper, what type of rigid motion has occurred?

Which of the following is NOT a rigid motion?

Jill and Jane sit next to each other in math class. Jill has a sheet of paper and Jane asks her for half of it to take notes on because she left her notebook in the locker. If Jill cuts the sheet of paper in half, has a rigid motion occurred?

Jane and Bob are filling up water balloons for a party they are throwing. Jane thinks the balloons should have more water in them so she fills them fuller. Each water balloon's circumference is one inch greater than before. Does this describe a rigid motion?

Select the answer that best completes the following definition: A motion that preserves distance in the plane is called a __________.

Determine whether the statement is true or false. For a translation to be considered rigid, the starting and ending figures must be congruent.

has a rigid motion applied to it that results in . What can be concluded about the relationship between these two triangles.

has a rigid motion applied to it that results in . What can be concluded about the relationship between these two triangles.

Determine whether the statement is true or false: A glide reflection is a synonym for a rigid motion translation.

Determine whether the statement is true or false: All glide reflections are reflections.

A glide reflection is a rigid motion that occurs when a figure is translated a certain distance and then reflected or reflected and then translated. In either case, a glide reflection aways contains a reflection. Therefore, the statement, "All glide reflections are reflections." is true.

Sally has a quarter that is face up on the desk. If she slides it to Bob on the other side of the desk and he flips it over so that the tails side is facing up, is it a rigid motion?

Sally has a quarter that is face up on the desk. Then she slides the coin to Bob on the other side of the desk and he flips it over so that the tails side is facing up. What type of rigid motion does this situation describe?

Jenny has drawn a rectangle in the upper left hand corner of a piece of paper. If she folds the paper in half and traces the rectangle on the other half of the paper, what type of rigid motion has occurred?

Which of the following is NOT a rigid motion?

Jill and Jane sit next to each other in math class. Jill has a sheet of paper and Jane asks her for half of it to take notes on because she left her notebook in the locker. If Jill cuts the sheet of paper in half, has a rigid motion occurred?

Jane and Bob are filling up water balloons for a party they are throwing. Jane thinks the balloons should have more water in them so she fills them fuller. Each water balloon's circumference is one inch greater than before. Does this describe a rigid motion?

Select the answer that best completes the following definition: A motion that preserves distance in the plane is called a __________.

Determine whether the statement is true or false. For a translation to be considered rigid, the starting and ending figures must be congruent.

has a rigid motion applied to it that results in . What can be concluded about the relationship between these two triangles.

has a rigid motion applied to it that results in . What can be concluded about the relationship between these two triangles.

Select the answer that best completes the following definition:

A motion that preserves distance in the plane is called a __________.

Determine whether the statement is true or false.

For a translation to be considered rigid, the starting and ending figures must be congruent.

$\bigtriangleup ABC$ has a rigid motion applied to it that results in $\bigtriangleup A'B'C'$ . What can be concluded about the relationship between these two triangles.

$\bigtriangleup ABC$ has a rigid motion applied to it that results in $\bigtriangleup A'B'C'$ . What can be concluded about the relationship between these two triangles.

Determine whether the statement is true or false:

A glide reflection is a synonym for a rigid motion translation.

Determine whether the statement is true or false:

All glide reflections are reflections.

A glide reflection is a rigid motion that occurs when a figure is translated a certain distance and then reflected or reflected and then translated. In either case, a glide reflection aways contains a reflection.

Therefore, the statement, "All glide reflections are reflections." is true.

Select the answer that best completes the following definition:

A motion that preserves distance in the plane is called a __________.

Determine whether the statement is true or false.

For a translation to be considered rigid, the starting and ending figures must be congruent.

$\bigtriangleup ABC$ has a rigid motion applied to it that results in $\bigtriangleup A'B'C'$ . What can be concluded about the relationship between these two triangles.

$\bigtriangleup ABC$ has a rigid motion applied to it that results in $\bigtriangleup A'B'C'$ . What can be concluded about the relationship between these two triangles.