Transcript Segment and Angle Bisectors

Segment and Angle
Bisectors
During today’s lesson, you will:
 bisect a segment
 bisect an angle
 solve problems involving
segment and angle bisectors
Mrs. McConaughy
Geometry
1
DEFINITION: Midpoint
Recall, the midpoint of a segment is
___________________________________
a point which divides (or bisects) the
segment into two congruent segments.
___________________________________.
A segment bisector is _________________
a segment, ray, line,
or plane which intersects a segment at its
___________________________________
midpoint
___________________________________.
Mrs. McConaughy
Geometry
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Draw a segment bisector given
AY with midpoint M.
How many segment bisectors can
be drawn through the midpoint M?
A
M
Mrs. McConaughy
Geometry
Y
3
DEFINITION: Perpendicular
Lines
Perpendicular lines ___________________
are two lines that
intersect
to form congruent right angles.
___________________________________.
Mrs. McConaughy
Geometry
4
Origami Exploration: Paper
Folding Perpendicular Bisectors
Step 1: On a piece of paper, draw HT.
Step 2: Fold the paper so that B is on
top of A.
Step 3: Label the point where the fold
intersects HT as point O.
Step 4: Measure HO and HT.
Step 5: Measure the four angles which
are formed.
Mrs. McConaughy
Geometry
5
DEFINITION:
Perpendicular
You are now ready
to write a good
definition of a perpendicular bisector.
Bisector
A perpendicular bisector of a segment is
__________________________________
a segment, ray or line which a. intersects
a segment at its midpoint and b. forms
___________________________________
congruent right angles.
___________________________________.
For additional information on paper-folding geometry,
click on the pencil in the upper right-hand corner.
Mrs. McConaughy
Geometry
6
Origami Exploration: Paper
Folding Angle Bisectors

Step 1: On a piece of paper, draw
ABC.
Step 2: Fold the paper so that CB is directly on
top of CA.
Step 3: Draw any point on the fold and label
the point D.
Step 4: Use a protractor to measure angles
ACD and BCD.
You are now ready to write a good
definition of an angle bisector.
Mrs. McConaughy
Geometry
7
DEFINITION: Angle Bisector
An angle bisector is __________________
a ray (or segment)
which
divides an angle into two congruent
___________________________________
angles.
The
vertex
of
the
segment
or
ray
is
___________________________________
at the angle’s vertex.
___________________________________.
Mrs. McConaughy
Geometry
8
Example: Finding Angle
Measures
The ray FH bisects angle EFG. Given
that m< EFG = 120, what are the
measures of the two angles which are
formed?
Mrs. McConaughy
Geometry
9
Example: Finding Angle
Measures
Given KN bisects angle JKL so that
m< JKN = 5x - 25 and m< KNL = 3x + 5.
Solve for x and find the measure of
< JKN.
Mrs. McConaughy
Geometry
10
Work Space:
Mrs. McConaughy
Geometry
11
Final Checks for Understanding
1. What two geometric figures are formed
when you paper-fold a perpendicular
bisector?
2. How do you indicate right angles in a
diagram?
3. Given QS is the bisector of < PQR,
determine m< SQR and m< PQR when
m < PQS = 40.
Mrs. McConaughy
Geometry
12
Homework Assignment
Pages 37-38: 9-12 all
OR
Segment and Angle
Bisectors WS
31 – 42 all; 44- 49 all
Mrs. McConaughy
Geometry
13