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.

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Presentation transcript:

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:

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.

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

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.

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

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

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

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

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