Section 6.6 Concurrence of Lines

1 / 6

# Section 6.6 Concurrence of Lines - PowerPoint PPT Presentation

Section 6.6 Concurrence of Lines. A number of lines are concurrent if they have exactly one point in common. m, n and p are concurrent. A. m. n. p. Concurrent lines in Triangles. Theorem 6.6.1: The three angle bisectors of the angles of a triangle are concurrent.

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

## PowerPoint Slideshow about 'Section 6.6 Concurrence of Lines' - rosalind

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

### Section 6.6 Concurrence of Lines

A number of lines are concurrent if they have exactly one point in common.

m, n and p are concurrent.

A

m

n

p

Section 6.6 Nack

Concurrent lines in Triangles
• Theorem 6.6.1: The three angle bisectors of the angles of a triangle are concurrent.
• The point at which the angle bisectors meet is the incenter of the triangle. It is the center of the inscribed circle of the triangle.

Section 6.6 Nack

Theorem 6.62: The three perpendicular bisectors of the sides of a triangle are concurrent.

The point at which the perpendicular bisectors of the sides of a triangle meet is the circumcenter (center of the circumscribed circle) of the triangle.

Perpendicular Bisectors

Section 6.6 Nack

Altitudes of a Triangle
• Theorem 6.63: The three altitudes of a triangle are concurrent.
• The point of concurrence for the three altitudes of a triangle is the orthocenter of the triangle.

Section 6.6 Nack

Medians

Theorem 6.6.4: The three medians of a triangle are concurrent at a point that is two-thirds the distance from any vertex to the midpoint of the opposite side. The point of concurrence for the three medians is the centroid of the triangle.

Reminder: A median joins a vertex to the midpoint of the opposite side of the triangle.

Section 6.6 Nack

Summary
• Summary of Chapter Six is on pages 329-330

Section 6.6 Nack