Title: Chapter 5 Properties of Triangles Perpendicular and Angle Bisectors Sec 5.1
1Chapter 5 Properties of Triangles Perpendicular
and Angle BisectorsSec 5.1
- Goal
- To use properties of perpendicular bisectors and
angle bisectors
2Perpendicular Bisector
Perpendicular Bisector a segment, ray, line, or
plane that is perpendicular to a segment at its
midpoint.
3Equidistant
Equidistant from two points means that the
distance from each point is the same.
4Perpendicular Bisector Theorem
Perpendicular Bisector Theorem If a point is on
the perpendicular bisector of a segment, then it
is equidistant from the endpoints of the segment.
5Converse of the Perpendicular Bisector Theorem
Converse of the Perpendicular Bisector Theorem
If a point is equidistant from the endpoints of a
segment, then it is on the perpendicular bisector
of a segment.
6Example
Does D lie on the perpendicular bisector of
7Example
8Distance from a point to a line
The distance from a point to a line is defined to
be the shortest distance from the point to the
line. This distance is the length of the
perpendicular segment.
9Angle Bisector Theorem
Angle Bisector Theorem If a point (D) is on
the bisector of an angle, then it is equidistant
from the two sides of the angle.
10Converse of the Angle Bisector Theorem
Converse of the Angle Bisector Theorem If a
point is on the interior of an angle, and is
equidistant from the sides of the angle, then it
lies on the bisector of the angle.
11Examples
Does the information given in the diagram allow
you to conclude that C is on the perpendicular
bisector of AB?
12Examples
Does the information given in the diagram allow
you to conclude that P is on the angle bisector
of angle A?
13Examples
Draw the segment that represents the distance
indicated.
R perpendicular to LM
T perpendicular to AP
14Examples
Name the segment whose length represents the
distance between M to AT T to HM H to MT