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## PowerPoint Slideshow about ' Special Segments of Triangles' - nicole

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### Special Segments of Triangles

Sections 5.2, 5.3, 5.4

Perpendicular bisector theorem

- A point is on the perpendicular bisector if and only if it is equidistant from the
- endpoints of the segment.

Angle Bisector Theorem

- A point is on the bisector of an angle if and only if it is equidistant from the two sides of the angle.

Medians of a triangle

- A median of a triangle is a segment from a vertex to the midpoint of the
- opposite side.

Altitudes of a triangle

- An altitude of a triangle is the perpendicular segment from a vertex to the
- opposite side or to the line that contains the opposite side.

Concurrency

- The point of intersection of the lines, rays, or segments is called the point of concurrency.

Points of concurrency

- The point of concurrency of the three perpendicular bisectors a triangle is called the circumcenter.
- The point of concurrency of the three angle bisectors of a triangle is called the incenter.
- The point of concurrency of the three medians of a triangle is called the centroid.
- The point of concurrency of the three altitudes of a triangle is called the orthocenter.
- The incenter and centroid will always be inside the triangle. The circumcenter
- and orthocenter can be inside, on, or outside the triangle.

What is special about the Circumcenter?

- The perpendicular bisectors of a triangle intersect at a point that is equisdistant
- from the vertices of the triangle.

PA = PB = PC

What is special about the Incenter?

- The angle bisectors of a triangle intersect at a point that is equidistant from the
- sides of the triangle.

PD = PE = PF

What is special about the Centroid?

- The medians of a triangle intersect at a point that is two thirds of the distance
- from each vertex to the midpoint of the opposite side.

What is special about the Orthocenter?

- There is nothing special about the point of concurrency of the altitudes of a
- triangle.

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