Perpendicular and Angle Bisectors Theorems
5-2
Perpendicular and Angle
Bisectors
A point is
equidistant
from two objects
if it is the same distance from the
objects
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
Problem 1: Using the Perpendicular
Bisector Theorem
Problem 2: Using a Perpendicular Bisector
A park director wants to build a T-shirt stand equidistant from
the Rollin’ Coaster and the Spaceship Shoot. What are the
possible locations of the stand? Explain.
Distance from a point to a line:
the length of the
perpendicular segment from the point to the line
The distance is also the length of the shortest
segment from the point to the line.
In the figure the distances from A to line
l
and from B
to
l
are represented by the red segments.
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 Theorem
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
Problem 3: Using the Angle Bisector
Theorem
Explore the Perpendicular and Angle Bisector Theorems through images and explanations. Understand the concepts of equidistance, distance from a point to a line, and the implications of these theorems in geometry problems.
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Presentation Transcript
5-2 Perpendicular and Angle Bisectors
A point is equidistant from two objects if it is the same distance from the objects
Perpendicular Bisector Theorem If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment
Problem 1: Using the Perpendicular Bisector Theorem
Problem 2: Using a Perpendicular Bisector A park director wants to build a T-shirt stand equidistant from the Rollin Coaster and the Spaceship Shoot. What are the possible locations of the stand? Explain.
Distance from a point to a line: the length of the perpendicular segment from the point to the line The distance is also the length of the shortest segment from the point to the line. In the figure the distances from A to line l and from B to l are represented by the red segments.
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 Theorem 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
