Wyoming Math G.CO.9
The Standard
Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.
2023 Wyoming Mathematics Content and Performance Standards · Prove geometric theorems.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students prove angle relationships using facts they already know, such as angles on a straight line add to 180 degrees. They also show why a point is equally far from both ends of a segment if and only if it lies on the segment’s perpendicular bisector.
What Mastery Looks Like
- A student can prove that opposite angles formed by crossing lines are equal. Given parallel lines and a transversal, they can justify equal alternate interior or corresponding angles. They can prove both directions of the perpendicular bisector claim.
Common Misconceptions
- Students may call adjacent angles vertical angles. They may assume alternate interior angles are equal even when the lines are not parallel. Some think the midpoint is the only point equally far from both endpoints.
How to Assess It
- Draw two crossing lines and label one angle 65 degrees. Ask students to prove the opposite angle is 65 degrees using angles on a straight line, not a protractor.
Lesson moves
Ways to Teach It
Fold paper so endpoints A and B of a drawn segment meet, mark point P on the crease, then explain why PA equals PB.
Write a two-column proof that vertical angles are equal using two linear pairs, then explain why a protractor reading is not proof.
Give partners six diagram cards showing intersecting lines or transversals; have them sort angle claims by whether parallel lines are needed.
On a map, mark two bus stops A and B; find sites equally far from both and explain why they lie on the perpendicular bisector.
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