Section 4.7 Medians, Altitudes, and Perpendicular Bisectors

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Section 4.7 Medians, Altitudes, and
Perpendicular Bisectors
WARM UP
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Activity Part 1

1. Draw a triangle.
2. Label it ?BOY.
3. Measure each side of the triangle.
4. Find and mark the MIDPOINT of each side.

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Activity Part 2

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

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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.

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What is a Centroid?

• Centroid the point where all three medians meet
• The medians of a triangle divide one another into
  ratios of 21.

x 6
x
y
3
11
y 5.5
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Activity 2

1. Draw a triangle.
2. Label it ? WIG.
3. Draw a segment from W to the opposite side so
   that it makes a right angle with that side.

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What is an Altitude?

• The perpendicular segment from a vertex to the
  opposite side.
• Altitudes can be drawn OUTSIDE of the triangle.

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• Orthocenter point where three altitudes meet

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

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Perpendicular Bisectors

• What is true of AB and AC?

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• Circumcenter point where three perpendicular
  bisectors meet.

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TOGETHER, OPEN YOUR TEXTBOOK

• Page 155 - Classroom Exercises
• 1-6

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Partner Practice

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