1 / 11

# Special Segments of Triangles - PowerPoint PPT Presentation

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

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

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Special Segments of Triangles

Sections 5.2, 5.3, 5.4

• A point is on the perpendicular bisector if and only if it is equidistant from the

• endpoints of the segment.

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

• A median of a triangle is a segment from a vertex to the midpoint of the

• opposite side.

• 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.

• The point of intersection of the lines, rays, or segments is called the point 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

• 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.

• There is nothing special about the point of concurrency of the altitudes of a

• triangle.