5-1 Bisectors, Medians, And Altitudes

5-1 Bisectors, Medians, and Altitudes

Lil’ Wayne Sez Most things in Geometry make perfect sense…. ….it’s just hard to explain them.

Check this out! Today we will go over the definitions, but then Mr. A will draw them LIVE

Perpendicular Bisector is what it says.

Any point on the perpendicular bisector is the same distance from the ends of the segment being bisected. !

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In a triangle, there are three perpendicular bisectors.

Where they meet is called the circumcenter

Check this out: The circumcenter of a triangle is automatically the same distance from its vertices! NO MATTER WHAT!! (Mr. A must minimize now, and go to the program to show you, so remind him because he is kinda slow…)

Angle Bisector

If you have an angle bisector in a triangle, then it is the same distance from both of the sides of the angle.

A triangle has three anglebisectors as well. Where they meet is called the incenter.

The incenter of a triangle is always the same distance from the sides, NO MATTER WHAT!

(Mr. A will now minimize)

• A Median is a segment that has endpoints at a vertex and the midpoint of the opposite side in a triangle. a triangle has three of these as well. M ED

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• And, of course, there’s a special name for where the medians meet…CENTROID.

What’s special about the centroid, Mr. A ?

The Centroid is always I’m Glad You Asked! 2/3 of the total distance from the vertex to the other side! 2/3

For Example: If G is the centroid, and GE = 6, how long is BE ?

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B

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GE = (2/3)BE 6 = (2/3)BE 6(3/2) = BE 9 = BE

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The altitude is a segment from the vertex of a triangle to the opposite side that is perpendicular to that side.

ORTHOCENTER

• There is nothing special about the orthocenter. ..but you will be asked to find it…