Honors Geometry Intro. to Geometric Proofs. Before we can consider geometric proofs, we need to review important definitions and postulates from Unit.

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Presentation transcript:

Honors Geometry Intro. to Geometric Proofs

Before we can consider geometric proofs, we need to review important definitions and postulates from Unit I. “If and only if” (abbreviated iff) means that both a statement and its converse is true.

Definitions:

An angle is a right angle iff Two lines are perpendicular iff it has a measure of 90 degrees. they intersect to form a right angle.

A ray bisects an angle iff the ray divides the angle into two congruent angles.

Two angles are complementary iff Two angles are supplementary iff they have a sum of 90 degrees. they have a sum of 180 degrees.

A point is a midpoint of a segment iff the point divides the segment into two congruent segments.

You must also be able to use the definition of a linear pair to identify a linear pair in a figure.

Postulates:

Segment Addition Postulate: If R is between P and Q, then PR + RQ = PQ

Angle Addition Postulate: If S is in the interior of, then

Linear Pair Postulate: If two angles form a linear pair, then the angles are supplementary.

Examples: Complete, and give a reason for, each statement. Defintion of angle bisector Definition of complementary

Examples: Complete, and give a reason for, each statement. Definition of right angle Definition of perpendicular

Examples: Complete, and give a reason for, each statement. Definition of midpoint

Example: Complete this partial proof. Given Def. of Perpendicular Def. of right angle Angle Addition Post. Substitution prop. Def. of complementary