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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 it has a measure of 90 degrees. Two lines are perpendicular iff 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 they have a sum of 90 degrees. Two angles are supplementary iff 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 PQR , then mPQS mSQR mPQR Linear Pair Postulate: If two angles form a linear pair, then the angles are supplementary. Examples: Complete, and give a reason for, each statement. FMD DMC Defintion of angle bisector mFME mBMC 90 Definition of complementary Examples: Complete, and give a reason for, each statement. mEMC 90 Definition of right angle ME MC Definition of perpendicular Examples: Complete, and give a reason for, each statement. AM MC Definition of midpoint Example: Complete this partial proof. JG JI mGJI 90 1 and 2 are complement ary Given Def. of Perpendicular Def. of right angle Angle Addition Post. Substitution prop. Def. of complementary