Subjects geometry

Line Relations 2D9A5A

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1. **Stating the problem:** We are given three line segments/rays OP, QR, and MN intersecting at the center. We need to determine which statement is true among: - OP is perpendicular to QR. - MN is perpendicular to QR. - MN is parallel to OP. 2. **Understanding the problem:** - Two lines are perpendicular if the angle between them is 90 degrees. - Two lines are parallel if they have the same slope (direction) and never intersect except possibly at infinity. 3. **Analyzing the given information:** - QR is a steep diagonal line from top-left to bottom-right. - OP is a shallow line from left to right. - MN is a diagonal line from bottom-left to top-right. 4. **Checking perpendicularity:** - OP and QR have very different slopes, but not necessarily perpendicular. - MN and QR are diagonal lines in opposite directions, but not necessarily perpendicular. 5. **Checking parallelism:** - OP and MN both appear to be diagonal lines slanting in the same direction (bottom-left to top-right), suggesting they are parallel. 6. **Conclusion:** - The true statement is **MN is parallel to OP**. **Final answer:** MN is parallel to OP.
MNOPQR