December 7, 2016 5-2: Perpendicular and Angle Bisectors Geometry December 7, 2016 5-2: Perpendicular and Angle Bisectors

DO NOW 𝐴𝐶 is parallel to… If AB = 10, then YZ = If XY = 13, then BZ = What is the midpoint of 𝐴𝐵 ?

Agenda Announcements (2nd hour only) Do Now Review Notes Practice

I can identify and apply triangle midsegments, medians, and altitudes.

Midsegment Properties A midsegment is exactly half the length of its parallel side.

Perpendicular Bisector Bisector: Cuts into congruent parts Perpendicular: Forms a right angle

Perpendicular Bisector If 𝐶𝐷 is the perpendicular bisector of 𝐴𝐵 , then 𝐴𝐶 ≅ 𝐵𝐶 .

C is the same distance from A and B, so it is EQUIDISTANT to A and B.

PRACTICE: Calculate x

PRACTICE: Calculate n

Angle Bisector Angle Bisector: A ray which divides an angle into two congruent angles.

Angle Bisector Every point on an angle bisector is equidistant to the two sides of the angle.

Angle Bisector 𝑚∠𝑆𝑄𝑃≅𝑚∠𝑆𝑄𝑅⇔ 𝑆𝑃 ≅ 𝑆𝑅

PRACTICE: Calculate x

PRACTICE: Calculate x

KEY TAKEAWAY Perpendicular and angle bisectors create CONGRUENT SEGMENTS because ALL POINTS along a bisecting line are equidistant.

ADDITIONAL PRACTICE