Understanding Segment and Angle Bisectors in Geometry
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In today's lesson, we will explore the concepts of segment and angle bisectors. You will learn how to bisect a segment and an angle, solve related problems, and understand the definitions and properties of these geometric figures. We will also engage in hands-on activities, including origami folding, to visualize perpendicular and angle bisectors. By the end of the lesson, you will be equipped to identify and use bisectors in various geometry problems.
Understanding Segment and Angle Bisectors in Geometry
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Presentation Transcript
Segment and Angle Bisectors During today’s lesson, you will: bisect a segment bisect an angle solve problems involving segment and angle bisectors Geometry
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
Draw a segment bisector given AY with midpoint M. How many segment bisectors can be drawn through the midpoint M? A M Y Geometry
DEFINITION:Perpendicular Lines Perpendicular lines ___________________ ___________________________________. are two lines that intersect to form congruent right angles. Geometry
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
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
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
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
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
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
Work Space: Geometry
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
Homework Assignment Pages 37-38: 9-12 all OR Segment and Angle Bisectors WS 31 – 42 all; 44- 49 all Geometry
