Chapter 1
Number & Quantity and Algebra
Course: Praxis Mathematics 5165
Subject: Praxis Study Companion Mathematics 5165
Chapter: Geometry
Knows the Properties of Lines and Angles
Lines and angles form the core structure of plane geometry. Many geometry problems reduce to identifying how lines relate (parallel, perpendicular, intersecting) and then using angle relationships created by intersections and transversals. In coordinate geometry, slope becomes the tool that replaces visual reasoning, allowing you to prove parallelism and perpendicularity algebraically.
Solves Problems Involving Parallel, Perpendicular, and Intersecting Lines
Parallel lines are lines in a plane that never meet and remain the same distance apart. Perpendicular lines intersect to form right angles (90°). Intersecting lines meet at a point but not necessarily at a right angle. In the coordinate plane, slopes provide a reliable method for confirming these relationships:
- Parallel: same slope, different intercepts (or the same line)
- Perpendicular: slopes are negative reciprocals, meaning m1m2=−1(when both slopes are defined)
- Intersecting but not perpendicular: slopes are different but not negative reciprocals