Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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Hi, does anyone know the answer to this question? I’m bad at geometry and I’m struggling to answer it.
### Geometry Problem: Parallel Line Construction **Problem Statement:** The diagram below illustrates the construction of line segment \(\overline{PS}\) parallel to \(\overline{RQ}\) through point \(P\). **Diagram Breakdown:** - A transversal line intersects two parallel lines. - \(P\) and \(S\) are points on one parallel line. - \(R\) and \(Q\) are points on the other parallel line. - Angles are marked as \(\angle 1\), \(\angle 2\), and \(\angle 3\), created by the intersection of the transversal with the lines. ```plaintext The diagram below illustrates the construction of \overline{PS} parallel to \overline{RQ} through point P. P / \ / \ \_1_ S Q___________R / / / / 9_2_ / 3 ``` **Question:** Which statement justifies this construction? 1. \( \text{m}\angle 1 = \text{m}\angle 2 \) 2. \( \text{m}\angle 1 = \text{m}\angle 3 \) 3. \( \overline{PR} \equiv \overline{RQ} \) 4. \( \overline{PS} \equiv \overline{RQ} \) #### Explanation of Options: 1. \( \text{m}\angle 1 = \text{m}\angle 2 \) - This indicates that angles 1 and 2 are equal, suggesting alternate interior angles. 2. \( \text{m}\angle 1 = \text{m}\angle 3 \) - This indicates that angles 1 and 3 are equal, suggesting corresponding angles. 3. \( \overline{PR} \equiv \overline{RQ} \) - This indicates that line segments \(PR\) and \(RQ\) are congruent. 4. \( \overline{PS} \equiv \overline{RQ} \) - This indicates that line segments \(PS\) and \(RQ\) are congruent. **Conclusion:** The correct answer is option 2: \( \text{m}\angle 1 = \text{m}\angle 3 \). This is the criterion for
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Transcribed Image Text:### Geometry Problem: Parallel Line Construction **Problem Statement:** The diagram below illustrates the construction of line segment \(\overline{PS}\) parallel to \(\overline{RQ}\) through point \(P\). **Diagram Breakdown:** - A transversal line intersects two parallel lines. - \(P\) and \(S\) are points on one parallel line. - \(R\) and \(Q\) are points on the other parallel line. - Angles are marked as \(\angle 1\), \(\angle 2\), and \(\angle 3\), created by the intersection of the transversal with the lines. ```plaintext The diagram below illustrates the construction of \overline{PS} parallel to \overline{RQ} through point P. P / \ / \ \_1_ S Q___________R / / / / 9_2_ / 3 ``` **Question:** Which statement justifies this construction? 1. \( \text{m}\angle 1 = \text{m}\angle 2 \) 2. \( \text{m}\angle 1 = \text{m}\angle 3 \) 3. \( \overline{PR} \equiv \overline{RQ} \) 4. \( \overline{PS} \equiv \overline{RQ} \) #### Explanation of Options: 1. \( \text{m}\angle 1 = \text{m}\angle 2 \) - This indicates that angles 1 and 2 are equal, suggesting alternate interior angles. 2. \( \text{m}\angle 1 = \text{m}\angle 3 \) - This indicates that angles 1 and 3 are equal, suggesting corresponding angles. 3. \( \overline{PR} \equiv \overline{RQ} \) - This indicates that line segments \(PR\) and \(RQ\) are congruent. 4. \( \overline{PS} \equiv \overline{RQ} \) - This indicates that line segments \(PS\) and \(RQ\) are congruent. **Conclusion:** The correct answer is option 2: \( \text{m}\angle 1 = \text{m}\angle 3 \). This is the criterion for
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