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Answer :
To determine which statement is true about the quadrilaterals WXYZ and W'X'Y'Z', let's break down what we're looking for:
1. Congruent Quadrilaterals: Two quadrilaterals are congruent if they have the same shape and size. This happens if you can map one quadrilateral to the other using a series of rigid motions.
2. Rigid Motions: These are transformations that preserve distance and angles, such as:
- Translations (sliding the shape around the plane without rotating it)
- Rotations (spinning the shape around a point)
- Reflections (flipping the shape over a line)
3. Applying the Concept:
- If there is a series of rigid motions that can perfectly map quadrilateral WXYZ onto quadrilateral W'X'Y'Z', then these two quadrilaterals are congruent. This means they have the same size and shape, even if their positions or orientations are different.
Now, let's evaluate the statements:
- First Statement: "Quadrilateral WXYZ is congruent to quadrilateral W'X'Y'Z' because there is a series of rigid motions that maps quadrilateral WXYZ onto quadrilateral W'X'Y'Z'."
- This statement is true. If you can use rigid motions to map one quadrilateral onto another, they are congruent.
- Other Statements: These involve either saying the quadrilaterals are congruent but with an incorrect reason (no rigid motions) or that they are not congruent due to either the presence or absence of rigid motions. These are incorrect based on our understanding of congruence.
Thus, the correct statement is that Quadrilateral WXYZ is congruent to quadrilateral W'X'Y'Z' because there is a series of rigid motions that maps quadrilateral WXYZ onto quadrilateral W'X'Y'Z'.
1. Congruent Quadrilaterals: Two quadrilaterals are congruent if they have the same shape and size. This happens if you can map one quadrilateral to the other using a series of rigid motions.
2. Rigid Motions: These are transformations that preserve distance and angles, such as:
- Translations (sliding the shape around the plane without rotating it)
- Rotations (spinning the shape around a point)
- Reflections (flipping the shape over a line)
3. Applying the Concept:
- If there is a series of rigid motions that can perfectly map quadrilateral WXYZ onto quadrilateral W'X'Y'Z', then these two quadrilaterals are congruent. This means they have the same size and shape, even if their positions or orientations are different.
Now, let's evaluate the statements:
- First Statement: "Quadrilateral WXYZ is congruent to quadrilateral W'X'Y'Z' because there is a series of rigid motions that maps quadrilateral WXYZ onto quadrilateral W'X'Y'Z'."
- This statement is true. If you can use rigid motions to map one quadrilateral onto another, they are congruent.
- Other Statements: These involve either saying the quadrilaterals are congruent but with an incorrect reason (no rigid motions) or that they are not congruent due to either the presence or absence of rigid motions. These are incorrect based on our understanding of congruence.
Thus, the correct statement is that Quadrilateral WXYZ is congruent to quadrilateral W'X'Y'Z' because there is a series of rigid motions that maps quadrilateral WXYZ onto quadrilateral W'X'Y'Z'.
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