Geometric Proofs

Build short proofs using diagrams, definitions, and theorems.

Lesson 5 of 53 parts Practice Flashcards

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Angle Relationships in Proofs

Objective: Use vertical angles and linear pairs with justified reasons.

Vertical angles are congruent. A linear pair has measures summing to 180°. Angle addition applies when a ray lies in an angle’s interior. State the configuration before using a relationship.

Two intersecting lines: angles 1 and 3 are vertical and congruent; angles 1 and 2 form a linear pair summing to 180 degrees.

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Angle Relationships in Proofs

Objective: Use vertical angles and linear pairs with justified reasons.

Vertical angles are congruent. A linear pair has measures summing to 180°. Angle addition applies when a ray lies in an angle’s interior. State the configuration before using a relationship.

Segment Relationships in Proofs

Objective: Use midpoint and segment addition definitions.

A midpoint lies on a segment and creates two congruent subsegments. If B lies between A and C, then AB+BC=AC. A segment bisector meets a segment at its midpoint.

Segment AC with midpoint M; matching tick marks show AM congruent to MC, and AM plus MC equals AC.

Proof Structure

Objective: Identify givens, a goal, and a valid chain of reasons.

A geometric proof begins with givens and derives the desired conclusion through definitions, postulates, and theorems. Diagram appearance alone is not a valid justification unless supported by given facts.

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