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

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A segment bisector is _________________

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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 ___________________

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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

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___________________________________.

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 __________________

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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 11

Work Space:

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.

Mrs. McConaughy Geometry 13

Homework Assignment

Pages 37-38: 9-12 all

OR

Segment and Angle Bisectors WS

31 – 42 all; 44- 49 all