# 1 Aim: How do we prove lines are perpendicular? Do Now: A C D B StatementsReasons 1) 2) 3) 4) 5) 6) 7) 8) Given Def. Linear pair Linear pair is suppl.

Perpendicular Lines and Linear Pairs of Congruent Angles Proof
Perpendicular Lines and Linear Pairs of Congruent Angles Proof

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1 Aim: How do we prove lines are perpendicular? Do Now: A C D B StatementsReasons 1) 2) 3) 4) 5) 6) 7) 8) Given Def. Linear pair Linear pair is suppl. Def. supplementary Substitution Postulate Division Postulate Substitution Postulate Prove: Def. perpendicular Given:

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2Geometry Lesson: Proving Lines are Perpendicular Theorem #9: If two intersecting lines form congruent, adjacent angles, then the lines are perpendicular. A D C B Ex: Given Prove: StatementsReasons 1) 2) 3) 4) 5) Given Reflexive Postulate S.A.S. Postulate C.P.C.T.C.

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3Geometry Lesson: Proving Lines are Perpendicular Equidistant : X Y P What is true if P is equidistant from X and Y? P is the same distance from X and Y. PX = PY

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4Geometry Lesson: Proving Lines are Perpendicular AB D C p Def: Perpendicular Bisector The perpendicular bisector of a line segment is a line, line segment or ray that is perpendicular to the line segment and bisects it.

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5Geometry Lesson: Proving Lines are Perpendicular C AB Constructing a Perpendicular Bisector D

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6Geometry Lesson: Proving Lines are Perpendicular Theorem #10: If two points are each equidistant from the endpoints of a line segments, then the points determine the perpendicular bisector of the line segment. (Perpendicular Bisector Theorem) C AB D

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7Geometry Lesson: Proving Lines are Perpendicular Ex: Perpendicular Bisector Theorem StatementsReasons 1) 2) 3) 4) 5) Given M Q T B Given: Prove: C.P.C.T.C Perpendicular Bisector Theorem

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8Geometry Lesson: Proving Lines are Perpendicular Proving lines perpendicular: S T Q K 1) Given: Prove: G DR Q 2) Given: Prove:

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9Geometry Lesson: Proving Lines are Perpendicular Algebra w/perpendicular lines: S N D Z

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