# Section 4.7 Medians, Altitudes, and Perpendicular Bisectors - PowerPoint PPT Presentation

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## Section 4.7 Medians, Altitudes, and Perpendicular Bisectors

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### 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. – PowerPoint PPT presentation

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Title: Section 4.7 Medians, Altitudes, and Perpendicular Bisectors

1
Section 4.7 Medians, Altitudes, and
Perpendicular Bisectors
WARM UP
2
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.

3
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.

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 21.

x 6
x
y
3
11
y 5.5
6
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.

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