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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. DEFINITION: Midpoint. Recall, the midpoint of a segment is ___________________________________ ___________________________________.

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Segment and Angle Bisectors

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

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

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

  5. 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. Geometry

  6. DEFINITION:Perpendicular Bisector You are now ready to write a good definition of a perpendicular 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. 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 good definition of an angle bisector. 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. Geometry

  9. 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? 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. Geometry

  11. Work Space: Geometry

  12. Final Checks for Understanding • What two geometric figures are formed when you paper-fold a perpendicular bisector? • How do you indicate right angles in a diagram? • Given QS is the bisector of < PQR, determine m< SQR and m< PQR when m < PQS = 40. Geometry

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

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