Question
Which figure is similar to the parallelogram? (Figures may not be drawn to scale.)
A parallelogram has side lengths of 8 and 5.8. Angles are 68 degrees and 112 degrees.
A parallelogram has side lengths of 4 and 4.8. Angles are 68 degrees and 112 degrees.
A rectangle has a length of 6 and width of 4.8. All angles are 90 degrees.
A parallelogram has side lengths of 4 and 2.9. Angles are 48 degrees and 132 degrees.
A parallelogram has side lengths of 4 and 2.9. Angles are 68 degrees and 112 degrees.
A parallelogram has side lengths of 8 and 5.8. Angles are 68 degrees and 112 degrees.
A parallelogram has side lengths of 4 and 4.8. Angles are 68 degrees and 112 degrees.
A rectangle has a length of 6 and width of 4.8. All angles are 90 degrees.
A parallelogram has side lengths of 4 and 2.9. Angles are 48 degrees and 132 degrees.
A parallelogram has side lengths of 4 and 2.9. Angles are 68 degrees and 112 degrees.
Answers
GPT-4o mini
To determine which figure is similar to the given parallelogram with side lengths of \(8\) and \(5.8\) and angles of \(68^\circ\) and \(112^\circ\), we need to look for a figure that has the same angle measures and the same ratio of corresponding side lengths.
1. **Figure 1**: Parallelogram with sides \(4\) and \(4.8\) and angles \(68^\circ\) and \(112^\circ\).
- Angles match with the original parallelogram.
- Ratio of sides: \(4/8 = 0.5\) and \(4.8/5.8 \approx 0.8276\). **Not similar**.
2. **Figure 2**: Rectangle with length \(6\) and width \(4.8\), all angles \(90^\circ\).
- Angles do not match. **Not similar**.
3. **Figure 3**: Parallelogram with sides \(4\) and \(2.9\) and angles \(48^\circ\) and \(132^\circ\).
- Angles do not match. **Not similar**.
4. **Figure 4**: Parallelogram with sides \(4\) and \(2.9\) and angles \(68^\circ\) and \(112^\circ\).
- Angles match with the original parallelogram.
- Ratio of sides: \(4/8 = 0.5\) and \(2.9/5.8 = 0.5\). **Similar**, since both side ratios are \(0.5\).
Based on this analysis, the figure that is similar to the given parallelogram is:
**A parallelogram has side lengths of 4 and 2.9. Angles are 68 degrees and 112 degrees.**
1. **Figure 1**: Parallelogram with sides \(4\) and \(4.8\) and angles \(68^\circ\) and \(112^\circ\).
- Angles match with the original parallelogram.
- Ratio of sides: \(4/8 = 0.5\) and \(4.8/5.8 \approx 0.8276\). **Not similar**.
2. **Figure 2**: Rectangle with length \(6\) and width \(4.8\), all angles \(90^\circ\).
- Angles do not match. **Not similar**.
3. **Figure 3**: Parallelogram with sides \(4\) and \(2.9\) and angles \(48^\circ\) and \(132^\circ\).
- Angles do not match. **Not similar**.
4. **Figure 4**: Parallelogram with sides \(4\) and \(2.9\) and angles \(68^\circ\) and \(112^\circ\).
- Angles match with the original parallelogram.
- Ratio of sides: \(4/8 = 0.5\) and \(2.9/5.8 = 0.5\). **Similar**, since both side ratios are \(0.5\).
Based on this analysis, the figure that is similar to the given parallelogram is:
**A parallelogram has side lengths of 4 and 2.9. Angles are 68 degrees and 112 degrees.**