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Lesson 32 Median, Angle Bisector, Altitude and

Perpendicular Bisector

- Nov. 13, 2009

Homework

- Geometry, P156-158, 7-17, 19, 23

Do Now

- Suppose that you and Pat are partners in a game

in which you must locate various clues to win.

You are told to pick up your next clue at a point

that - is as far from the fountain as from the oak tree
- and
- is 10 m from the flag pole.
- Q Can you find a point that meets both

requirements 1 and 2?

Question

- What kinds of segments can you draw from a vertex

to the opposite side in a triangle?

Vocabulary

- Median of a triangle a segment from a vertex to

the midpoint of the opposite side. - Altitude of a triangle the perpendicular segment

from a vertex to the line that contains the

opposite side. (Q Is it important to mention the

line that contains the opposite side?)

Questions

- What kind of triangle has one angle bisector that

is also altitude and median? - What kind of triangle has three angle bisectors

that are also altitudes and medians?

Vocabulary

- Perpendicular bisector of a segment a line (or

ray or segment) that is perpendicular to the

segment at its midpoint. (Q Does perpendicular

bisector only exist in a triangle?)

Equidistance Theorems of Perpendicular Bisectors

- Theorem 4-5 If a point lies on the perpendicular

bisector of a segment, then the point is

equidistant from the endpoints of the segment. - Theorem 4-6 If a point is equidistant from the

endpoints of a segment, then the point lies on

the perpendicular bisector of the segment. - Q Can you combine both theorems into one

biconditional statement?

Example

- Given S is equidistant from E and D V is

equidistant from E and D. - Prove is the perpendicular bisector of

Equidistance Theorems of Angle Bisectors

- Theorem 4-7 If a point lies on the bisector of

an angle, then the point is equidistant from the

sides of the angle. - Theorem 4-8 If a point is equidistant from the

sides of an angle, then the point lies on the

bisector of the angle. - Q Can you combine both theorems into one

biconditional statement?

Example

- Given bisects ?ADE bisects ?DEC
- Prove bisects ?ABC

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