Unit 3 - Parallel and Perpendicular Lines

Description of Unit:  This topic expands the students’ understandings and skills related to parallel and perpendicular lines.  Students will use postulates and theorems to explore lines in a plane; use coordinate geometry to examine the lopes of parallel and perpendicular lines; use the Triangle-Angle Sum Theorem; and write equations using slope-intercept and point-slope forms.

Key Vocabulary:  alternate exterior angles, alternate interior angles, corresponding angles, exterior angle of a polygon, parallel lines, parallel planes, point-slope form, remote interior angles, same-side interior angles, skew lines, slope, slope-intercept form, transversal.

Common Core Content Standards:

G-CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

G-CO.C.9 Prove theorems about lines and angles.

G-CO.C.10 Prove theorems about triangles.

G-CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

G-CO.D.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

G-GPE.B.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problem (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

G-MG.A.3 Apply geometric methods to solve design problem (e.g, designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based one ratios).