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Mrs. McConaughy Geometry 1
Segment and Angle Segment and Angle BisectorsBisectors
During today’s lesson, you will: bisect a segment bisect an angle solve problems involving segment and angle bisectors
Mrs. McConaughy Geometry 2
DEFINITION: Midpoint
Recall, the midpoint of a segment is
___________________________________
___________________________________.
A segment bisector is _________________
___________________________________
___________________________________.
a point which divides (or bisects) the segment into two congruent segments.
a segment, ray, line, or plane which intersects a segment at its midpoint
Mrs. McConaughy Geometry 3
Draw a segment bisector given AY with midpoint M.
A M Y
How many segment bisectors can be drawn through the midpoint M?
Mrs. McConaughy Geometry 4
Perpendicular lines ___________________
___________________________________.
DEFINITION: Perpendicular Lines are two lines that intersect to form congruent right angles.
Mrs. McConaughy Geometry 5
Origami Exploration: Paper Folding Perpendicular BisectorsStep 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 6
DEFINITION: Perpendicular BisectorA perpendicular bisector of a segment is
__________________________________
___________________________________
___________________________________.
You are now ready to write a gooddefinition of a perpendicular bisector.
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 7
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 gooddefinition of an angle bisector.
Mrs. McConaughy Geometry 8
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 9
The ray FH bisects angle EFG. Given that m< EFG = 120, what are the measures of the two angles which are formed?
Example: Finding Angle Measures
Mrs. McConaughy Geometry 10
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 12
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.