To prove that a constructed line is parallel to a given line, you can follow these steps:
1. Show that same side interior angles are congruent:
- If the constructed line intersects the given line, identify the same side interior angles created by the constructed line and the given line.
- Use the properties of parallel lines (same side interior angles are supplementary) to show that the same side interior angles are congruent.
2. Show that corresponding angles are congruent:
- Identify the corresponding angles created by the constructed line and the given line.
- Use the properties of parallel lines (corresponding angles are congruent) to show that the corresponding angles are congruent.
3. Show that the transversal intersects both lines:
- Show that the constructed line intersects the given line at a single point.
- Show that the constructed line does not intersect the given line at any other point.
4. Show that same side exterior angles are congruent:
- Identify the same side exterior angles created by the constructed line and the given line.
- Use the properties of parallel lines (same side exterior angles are congruent) to show that the same side exterior angles are congruent.
By following these steps and using the properties of parallel lines, you can prove that a constructed line is parallel to a given line.
9.
How can you prove that a constructed line is parallel to a given line? Assume that the transversal line is not perpendicular to the other lines.
Show that same side interior angles are congruent.
Show that corresponding angles are congruent.
Show that the transversal intersects both lines.
Show that same side exterior angles are congruent.
1 answer