1. Mrs. McConaughyGeometry1 Segment and Angle Bisectors During today’s lesson, you will:  bisect a segment  bisect an angle  solve problems involving segment and angle bisectors

2. Mrs. McConaughyGeometry2 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

3. Mrs. McConaughyGeometry3 Draw a segment bisector given AY with midpoint M. A M Y How many segment bisectors can be drawn through the midpoint M?

4. Mrs. McConaughyGeometry4 Perpendicular lines ___________________ ___________________________________. DEFINITION: Perpendicular Lines are two lines that intersect to form congruent right angles.

5. Mrs. McConaughyGeometry5 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.

6. Mrs. McConaughyGeometry6 DEFINITION: Perpendicular Bisector A perpendicular bisector of a segment is __________________________________ ___________________________________ ___________________________________. You are now ready to write a good definition 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.

7. Mrs. McConaughyGeometry7 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.

8. Mrs. McConaughyGeometry8 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.

9. Mrs. McConaughyGeometry9 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

10. Mrs. McConaughyGeometry10 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.

11. Mrs. McConaughyGeometry11 Work Space:

12. Mrs. McConaughyGeometry12 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.

13. Mrs. McConaughyGeometry13 Homework Assignment Pages 37-38: 9-12 all OR Segment and Angle Bisectors WS 31 – 42 all; 44- 49 all