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Name:_________________________________ Special Steps in Proofs Date:_______ Period:_____ Ms. Anderle Special Steps in Proofs Perpendicular: 3 steps 1. AB CD 2. <CBA and <DBA are right angles 3. CBA DBA A 1. Given 2. Perpendicular lines form right angles 3. All right angles are congruent Bisectors: 2 steps (a bisector can divide an angle or a line segment. Look carefully) 1. AB bisects <CBD 2. CBA DBA A 1. Given 2. An angle bisector divides an angle into two congruent angles. Midpoint: 2 steps *A segment bisectors and a midpoint BOTH divide a segment into two congruent segments --but don’t say one name instead of the other! 1. AD is the midpoint of BC 2. BD DC S 1. Given 2. A midpoint divides a segment into two congruent segments. Overlapping Triangles: 4 steps to get the overlapping sides. The given sides are too short. 1. 2. 3. 4. AB CD BC BC AB BC CD BC AB CD S 1. Given 2. Reflexive Property 3. Addition Postulate 4. Substitution The given sides are too long: 4 steps 1. 2. 3. 4. AC DB BC BC AC BC DB BC AB CD S Remember: Too Short: Given, reflexive, addition substitution Too Long: Given, reflexive, subtraction, substitution 1. Given 2. Reflexive Property 3. Subtraction Postulate 4. Substitution For supper, we need: 1) Milk 2) Bread 3) Eggs Supplementary Angles: 3 steps (look for an extended straight line) 1. 1 2 2. <1 & <3 are supplementary <2 & <4 are supplementary 3. 3 4 S 1. Given 2. Angles from a linear pair are supplementary 3. Supplements of <’s are Remember: If you run out of givens, you have two choices: Intersecting lines form congruent vertical angles Reflexive Property