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△EFG is rotated −90 degrees (clockwise) to create △XYZ . Which of the following statements must be true?(1 point) Responses ∠F≅...
△EFG is rotated −90 degrees (clockwise) to create △XYZ . Which of the following statements must be true?(1 point) Responses ∠F≅∠Z angle upper F congruent to angle upper Z EG¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯ Modifying above upper E upper G with bar congruent to Modifying above upper X upper Y with bar ∠E≅∠X angle upper E congruent to angle upper X EF¯¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯
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Answered by
STAN: TWS, ZEROBASEONE, AND RIIZE 4 BETTER LIFE
1one answetr only
Answered by
GPT-4o mini
To analyze the rotation of triangle \( \triangle EFG \) by -90 degrees (clockwise) to create triangle \( \triangle XYZ \), we need to understand how the points transform under this rotation.
1. **Understanding the rotation**: A rotation of -90 degrees clockwise will change the position of the points as follows, assuming the origin (0,0) is the center of rotation:
- Point E will move to point X.
- Point F will move to point Y.
- Point G will move to point Z.
Using this transformation:
- The points with respect to their angles will behave as follows:
- \( \angle EFG \) will become \( \angle XYZ \).
- \( \angle EGF \) will become \( \angle YXZ \).
- \( \angle FEG \) will become \( \angle ZXY \).
2. **Comparing angles and sides**: After a -90 degrees rotation, the following can be inferred:
- **Angles**: The angles that once corresponded in triangle \( \triangle EFG \) will correspond to angles in \( \triangle XYZ \) (due to the property of rotation preserving angle measures).
- **Sides**: The lengths of the sides will remain congruent since rotation preserves lengths.
Now let's evaluate the statements provided:
1. \( \angle F \cong \angle Z \): **True**. After the rotation, angle F will correspond to angle Z.
2. \( \overline{EG} \cong \overline{XY} \): **True**. Side EG corresponds to side XY.
3. \( \angle E \cong \angle X \): **False**. Angle E corresponds to angle Y after rotation.
4. \( \overline{EF} \cong \overline{XZ} \): **False**. Side EF corresponds to side YZ after rotation.
In summary, the statements that must be true are:
- \( \angle F \cong \angle Z \)
- \( \overline{EG} \cong \overline{XY} \)
Thus, both statements 1 and 2 are true.
1. **Understanding the rotation**: A rotation of -90 degrees clockwise will change the position of the points as follows, assuming the origin (0,0) is the center of rotation:
- Point E will move to point X.
- Point F will move to point Y.
- Point G will move to point Z.
Using this transformation:
- The points with respect to their angles will behave as follows:
- \( \angle EFG \) will become \( \angle XYZ \).
- \( \angle EGF \) will become \( \angle YXZ \).
- \( \angle FEG \) will become \( \angle ZXY \).
2. **Comparing angles and sides**: After a -90 degrees rotation, the following can be inferred:
- **Angles**: The angles that once corresponded in triangle \( \triangle EFG \) will correspond to angles in \( \triangle XYZ \) (due to the property of rotation preserving angle measures).
- **Sides**: The lengths of the sides will remain congruent since rotation preserves lengths.
Now let's evaluate the statements provided:
1. \( \angle F \cong \angle Z \): **True**. After the rotation, angle F will correspond to angle Z.
2. \( \overline{EG} \cong \overline{XY} \): **True**. Side EG corresponds to side XY.
3. \( \angle E \cong \angle X \): **False**. Angle E corresponds to angle Y after rotation.
4. \( \overline{EF} \cong \overline{XZ} \): **False**. Side EF corresponds to side YZ after rotation.
In summary, the statements that must be true are:
- \( \angle F \cong \angle Z \)
- \( \overline{EG} \cong \overline{XY} \)
Thus, both statements 1 and 2 are true.
Answered by
GPT-4o mini
The statement that must be true is:
**\( \angle F \cong \angle Z \)**.
**\( \angle F \cong \angle Z \)**.
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