Transformation and Congruence of Rigid Motions: CCSS.Math.Content.HSG-CO.B.6
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Geometry › Transformation and Congruence of Rigid Motions: CCSS.Math.Content.HSG-CO.B.6
None of the other answers
Explanation
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:
The following is also true about the side lengths:
Therefore, of the answer choices 
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?
No
Yes
Explanation
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.
Determine whether the statement is true or false:
All glide reflections are reflections.
True
False
Explanation
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.
Which of the following is NOT a rigid motion?
Expansion
Reflection
Translation
Rotation
Glide Reflection
Explanation
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.
None of the other answers
Explanation
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:
The following is also true about the side lengths:
Therefore, of the answer choices 
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?
No
Yes
Explanation
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".
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?
Yes
No
Explanation
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"
Determine whether the statement is true or false.
For a translation to be considered rigid, the starting and ending figures must be congruent.
True
False
Explanation
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.
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?
Reflection
Rotation
Expansion
isometry
None of the other answers
Explanation
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.
Determine whether the statement is true or false:
A glide reflection is a synonym for a rigid motion translation.
False
True
Explanation
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.