G-CO.3.9

Prove theorems about lines and angles; use theorems about lines and angles to solve problems. 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.

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Formative Assessments
Formative Assessments
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Students are asked to prove that a point on the perpendicular bisector of a line segment is equidistant from the endpoints of the segment.
Equidistant Points
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Students are asked to find the measures of angles formed by two parallel lines and two transversals.
Finding Angle Measures – 3
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In a diagram involving two parallel lines and a transversal, students are asked to use rigid motion to prove that alternate interior angles are congruent.
Proving the Alternate Interior Angles Theorem
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Assessment Questions
Assessment Questions
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Math Literature
Math Literature
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This task presents a foundational result in geometry, presented with deliberately sparse guidance in order to allow a wide variety of approaches.
Tangent Lines and the Radius of a Circle
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This task is part of a series presenting important foundational geometric results and constructions which are fundamental for more elaborate arguments.
Points Equidistant from Two Points in the Plane
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The goal of this task is to prove congruence of vertical angles made by two intersecting lines and alternate interior angles made by two parallel lines cut by a transverse.
Congruent Angles Made by Parallel Lines and a Transverse