1

Objectives

• To define, draw, and list characteristics of:– Midsegments– Altitudes– Perpendicular Bisectors– Medians

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Medians of Triangles

• A median of a triangle is a segment whose endpoints are a vertex and the midpoint of the opposite side.

3

Perpendicular Bisector

• A perpendicular bisector passes through the midpoint of a segment at a right angle with that segment

4

Altitude of a Triangle

An altitude is the perpendicular segment from a vertex to the line containing the opposite side.

5

Angle Bisector

• An angle bisector connects a vertex to the opposite side and cuts the vertex angle into two halves.

6

Midsegments of Triangles

• A midsegment of a triangle is a segment connecting the midpoints of two sides

7

Triangle Midsegment Theorem

If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side, and is half its length.

8

Point of Concurrency Definition

• When three or more lines intersect in one point, they are concurrent. The point at which they intersect is the point of concurrency.

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Centroid

The point of concurrency of the medians of a triangle is the centroid. The centroid is also called the center of gravity because it is the point where a triangular shape will balance.

The centroid of a triangle is always located inside the triangle.

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Circumcenter (Perpendicular Bisectors)

The point of concurrency of the perpendicular bisectors of a triangle is the circumcenter of the triangle. The circumcenter is the center of the circle which passes around the outside of the triangle and through each vertex.

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Orthocenter (Altitudes)The point of concurrency of the

altitudes of a triangle is the orthocenter of the triangle.

The orthocenter is inside the triangle for an acute triangle, at the right angle for a right triangle, and outside the triangle for an obtuse triangle.

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Incenter (Angle Bisectors)

The point of concurrency of the angle bisectors of a triangle is the incenter of the triangle. The incenter is the center of the circle which lies inside the triangle and touches all three sides of the triangle. The incenter is always inside the triangle.

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For Exploration

http://www.keymath.com/x19398.xml

http://www.keymath.com/x23078.xml