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Section 4.7 Medians, Altitudes, and Perpendicular Bisectors

Section 4.7 Medians, Altitudes, and Perpendicular Bisectors. WARM UP. Activity Part 1. Draw a triangle. Label it ∆ BOY. Measure each side of the triangle. Find and mark the MIDPOINT of each side. Activity Part 2. Draw a line connecting Point B to the MIDPOINT on the OPPOSITE SIDE.

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Section 4.7 Medians, Altitudes, and Perpendicular Bisectors

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  1. Section 4.7 Medians, Altitudes, and Perpendicular Bisectors WARM UP

  2. Activity Part 1 • Draw a triangle. • Label it ∆BOY. • Measure each side of the triangle. • Find and mark the MIDPOINT of each side.

  3. Activity Part 2 • Draw a line connecting Point B to the MIDPOINT on the OPPOSITE SIDE. • Draw a line connecting Point O to the MIDPOINT on the OPPOSITE SIDE. • Draw a line connecting Point Y to the MIDPOINT on the OPPOSITE SIDE.

  4. What is a Median? • A segment from a vertex to the midpoint of the opposite side. • Always three medians. • See the medians for a given triangle.

  5. What is a Centroid? • Centroid: the point where all three medians meet • The medians of a triangle divide one another into ratios of 2:1. x = 6 x y 3 11 y = 5.5

  6. Activity 2 • Draw a triangle. • Label it ∆ WIG. • Draw a segment from W to the opposite side so that it makes a right angle with that side.

  7. What is an Altitude? • The perpendicular segment from a vertex to the opposite side. • Altitudes can be drawn OUTSIDE of the triangle.

  8. Orthocenter: point where three altitudes meet

  9. Which line is the median? Which line is the altitude? a b

  10. What are Perpendicular Bisectors? • A line or ray that is perpendicular to the segment at its midpoint. • Does NOT have to start at a VERTEX

  11. Perpendicular Bisectors • What is true of AB and AC?

  12. Circumcenter: point where three perpendicular bisectors meet.

  13. TOGETHER, OPEN YOUR TEXTBOOK • Page 155 - Classroom Exercises • #1-6

  14. Partner Practice • Page 157 # 19 (a, b, and c) • TO BE HANDED IN! Make it neat. • I only need one per group.

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