Chapter 5 Section 2 Perpendicular and Angle Bisectors
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Transcript of Chapter 5 Section 2 Perpendicular and Angle Bisectors
Chapter 5 Section 2 Perpendicular and Angle
Bisectors
Objectives Students will be able to:
• Use properties of perpendicular bisectors and angle bisectors
• Apply the theorems of perpendicular and angle bisectors
Essential Understanding There is a special relationship
between the points on the perpendicular bisector of a segment and the endpoints of the segment.
There is a special relationship between the points on a bisector of an angle and the sides of the angle.
Perpendicular Bisector What do you know about perpendicular
bisectors? A right angle is formed and it splits a
segment into two equal parts Equidistant: a point that is the same
distance from two objects Which points are equidistant in the picture
below?
Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment
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 the segment
Using the Perpendicular Bisector Theorem
What is the length of QR? How would you set up the problem?
Distance from a point to a line:• The length of the perpendicular segment
from the point to the line• Length of the shortest segment• The shortest distance between two points is
a straight line
Angle Bisector Theorem If a point is on the bisector of an
angle, then the point is equidistant from the sides of the angle
Converse of the Angle Bisector Thoerem
If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector.
What is the length of FB?
Homework Pg. 296 6-12 all, 16-22 all, 29-31 17 problems