Lesson 6-1 Medians.

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Presentation transcript:

Lesson 6-1 Medians

Ohio Content Standards:

Ohio Content Standards: Formally define geometric figures.

Ohio Content Standards: Formally define and explain key aspects of geometric figures, including: a. interior and exterior angles of polygons; b. segments related to triangles (median, altitude, midsegment); c. points of concurrency related to triangles (centroid, incenter, orthocenter, and circumcenter); d. circles (radius, diameter, chord, circumference, major arc, minor arc, sector, segment, inscribed angle).

Median

Median A segment that joins a vertex of the triangle and the midpoint of the side opposite that vertex.

Median A B D median BD C

A E B D C

A E B D C Find BE if AB = 18.

If CD = 2x + 5, BD = 4x – 1, and AE = 5x -2, find BE.

Centroid

The common point where the medians of a triangle intersect. Centroid The common point where the medians of a triangle intersect.

Centroid C A B D L E F centroid

Concurrent

When three or more lines or segments meet at the same point. Concurrent When three or more lines or segments meet at the same point.

Theorem 6-1

Theorem 6-1 The length of the segment from the vertex to the centroid is twice the length of the segment from the centroid to the midpoint.

Theorem 6-1 2x x

Y N P Q X M Z Find YQ if QM = 4.

Y N P Q X M Z If QZ = 18, what is ZN?

Assignment: Pgs. 231-233 8-18 all, 24-29 all