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1.5 – Segment and Angle Bisectors

Objective: Students will be able to bisect line segments and angles. 1.5 – Segment and Angle Bisectors. Vocabulary. Congruent – equal (use for geometry) ‏ Bisect – to split in two congruent parts Midpoint – the point that bisects a segment

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1.5 – Segment and Angle Bisectors

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  1. Objective: Students will be able to bisect line segments and angles 1.5 – Segment and Angle Bisectors

  2. Vocabulary • Congruent – equal (use for geometry)‏ • Bisect – to split in two congruent parts • Midpoint – the point that bisects a segment • Segment Bisector – a segment, line, ray, or plane that bisects a segment • Angle Bisector – a ray that bisects an angle • Midpoint Formula:

  3. Using the Midpoint Formula • Find the coordinates of the midpoint of a segment with the endpoints: (4, 3), (-2, -2)‏ • 4 + -2 = 2, • 2/2 = 1 • 3 + -2 = 1 • ½ leave as fraction (1, ½) • Find the coordinates of the other endpoint if the midpoint is (2, 4) and one endpoint is (-1, 7)‏ • Find the difference: (2 - -1 = 3, 4 – 7 = -3)‏ • Get other point: For 2, we subtracted 3 to get to -1, so + • 2 + 3 = 5 • For 4, we added 3 to 4, so subtract 3. • 4 – 3 = 1 • (5, 1)‏

  4. Example 3 • Find the other endpoint if you know the midpoint and one endpoint: • M (-10, -16), B(-1, 8)‏ • -10 - - 1 = -9 • -16 – 8 = -24 • Get other endpoint • -10 – 9 = -19 • -16 – 24 = - 40 • (-19, -40)‏

  5. Angle Bisectors • CL bisects <KLM • If m<KLM is 65, what is m<KLC? • 32.5 • If KLC = x + 40 and CLM = 3x – 20, what is x? • X + 40 = 3x – 20 • 60 = 2x • X = 30

  6. Assignment • p. 38-40 17-30all, 37-42all, 44-49all, 52 • SHOW WORK!!!

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