Geometry (Holt 3-4)K.Santos

Perpendicular Bisector Perpendicular bisector of a segment is a line perpendicular to a segment at the segment’s midpoint. (could be a segment or ray) s M t Line s is perpendicular to line t at it’s midpoint M

Distance from a point to a line The shortest segment from a point to a line is perpendicular to the line. Distance form a point to a line is the length of the perpendicular segment from the point to the line.

Theorem (3-4-1) If two intersecting lines form a linear pair of congruent angles, then the lines are perpendicular. Given: <1 and < 2 are a linear pair n Then: m ⊥ n 1 2 m

Perpendicular Transversal Theorem (3-4-2) In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other line. a b Given: a||b t ┴ a t Then: t ┴ b

Theorem (3-4-3) Theorem: If two coplanar lines are perpendicular to the same line, then the two lines are parallel to each other. Given: a ┴ t a b ┴ t Then: a||b b t

Proof of previous theorem

Theorem If two coplanar lines are parallel to the same line, then they are parallel to each other. t Given: a ||b a b ||c b Then: a || c c

Example:

Example Given the information below what can you conclude about lines a and d? a || b a b ┴ cb ┴ c c || d b a ___ d? c d Draw a picture with all the line in it and then make a conclusion about lines a and d. a ┴ da ┴ d

Proof