17. Angles 1 and 3 are called interior angles on the same side the transversal. a. If / || m, what is true about m(21)+ m(23)? b. Can you show the converse of the result in part a: that if your conclusion about m(4I)+ m(23) is satisfied, then I ||m?

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
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The text explains a geometry concept with an accompanying diagram.

**Text:**

17. Angles 1 and 3 are called *interior angles on the same side of the transversal*.

**Diagram Description:**

The diagram shows two parallel lines, labeled \( l \) and \( m \), with a transversal intersecting them. The transversal creates four angles at the intersections:

- Angle 1 is positioned on the upper left, between line \( l \) and the transversal.
- Angle 2 is adjacent to Angle 1, on the upper right side of the transversal, aligned with line \( l \).
- Angle 3 is on the lower left, between line \( m \) and the transversal.
- There is a fourth angle, opposite Angle 3 on line \( m \).

**Questions:**

a. If \( l \parallel m \), what is true about \( m(\angle 1) + m(\angle 3) \)?

b. Can you show the converse of the result in part a: that if your conclusion about \( m(\angle 1) + m(\angle 3) \) is satisfied, then \( l \parallel m \)?

This exercise explores the properties of interior angles on the same side of a transversal and their relationship in confirming parallel lines.
Transcribed Image Text:The text explains a geometry concept with an accompanying diagram. **Text:** 17. Angles 1 and 3 are called *interior angles on the same side of the transversal*. **Diagram Description:** The diagram shows two parallel lines, labeled \( l \) and \( m \), with a transversal intersecting them. The transversal creates four angles at the intersections: - Angle 1 is positioned on the upper left, between line \( l \) and the transversal. - Angle 2 is adjacent to Angle 1, on the upper right side of the transversal, aligned with line \( l \). - Angle 3 is on the lower left, between line \( m \) and the transversal. - There is a fourth angle, opposite Angle 3 on line \( m \). **Questions:** a. If \( l \parallel m \), what is true about \( m(\angle 1) + m(\angle 3) \)? b. Can you show the converse of the result in part a: that if your conclusion about \( m(\angle 1) + m(\angle 3) \) is satisfied, then \( l \parallel m \)? This exercise explores the properties of interior angles on the same side of a transversal and their relationship in confirming parallel lines.
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