Curriculum placement
Geometry. This describes the skill, not a learner estimate.
Proofs about lines and angles
Prove vertical-angle parallel-line and perpendicular-bisector relationships
Problem types
- Justify a line and angle proof step
- Write a two-column parallel-line angle proof
Builds on
- Writing and critiquing a geometric proof
- Supplementary, vertical, and adjacent angles · Earlier idea
Angle pair facts are used as reasons in proofs about lines cut by a transversal.
Leads to
- Proofs about triangles · Extend the idea
Equal alternate interior angles from a line parallel to one side are the key step in the proof that a triangle's angles total 180 degrees.
- Theorems about circles · See it applied
Angle relations from parallel lines and transversals are reasons in proofs of circle angle theorems.
- Constructions with compass and straightedge · See it applied
Points equidistant from two endpoints lie on the perpendicular bisector. That fact is why arcs of equal radius from both endpoints construct it.
Related skills
- Congruence criteria for triangles · Shared foundations
- Proofs that use coordinates · Shared foundations
- Why the circle and solid formulas hold · Shared foundations
- Proofs about parallelograms · Shared foundations
- Proving triangles similar · Shared foundations
Open the interactive map to explore lessons and skill connections.