Perpendicular Line Segments Geometry St Barnabas HS Bronx

Perpendicular Line Segments Geometry St. Barnabas HS Bronx, NY 1

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

Theorem: Ex: Given Prove: If two intersecting lines form congruent, adjacent angles, then the lines are perpendicular. D A Statements B C Reasons 1) 1) Given 2) 2) Reflexive Postulate 3) 3) S. A. S. Postulate 4) 4) C. P. C. T. C. 5) 5) 3

Equidistant: P X Y What is true if P is equidistant from X and Y? • P is the same distance from X and Y. • PX = PY • Geometry Lesson: Proving Lines are Perpendicular 4

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. D D A P B C 5

Constructing a Perpendicular Bisector D A B C 6

Theorem: 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) D A B C 7

Ex: Perpendicular Bisector Theorem Given: Prove: B M Q T Statements Reasons 1) 1) Given 2) 2) C. P. C. T. C 3) 4) 5) 4) Perpendicular Bisector Theorem 5) Perpendicular Bisector Theorem 8

Proving lines perpendicular: 1) Given: Prove: S T K Q D 2) Given: Prove: G R Q 9

Algebra with perpendicular lines: Z S D N 10