5-2 Median & Altitudes of Triangles

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Presentation transcript:

5-2 Median & Altitudes of Triangles The student will be able to: 1. Identify and use medians in triangles. 2. Identify and use altitudes in triangles.

Medians of Triangles A median is a line segment that connects a vertex of a triangle to the midpoint of the opposite side.

The three medians of a triangle intersect at the centroid of the triangle. Centroid Theorem – the centroid is located two thirds of the distance from a vertex to the midpoint of the side opposite the vertex on a median. ⅓ ⅔ B L F

In ΔABC, U is the centroid and . Find each measure.

You need to know the following chart You need to know the following chart. For each segment, you should know the name of the point of concurrency and be able to construct an example. Also, know the special properties as they relate to solving problems.

An altitude of a triangle is a segment from a vertex to the line containing the opposite side and perpendicular to the line containing the opposite side. Every triangle has three altitudes that meet at a point called the orthocenter.

Examples: 1. Find x if is a median of ΔPQR.

2. If is a median of ΔMNQ, and find the value of a. Is also an altitude of ΔMNQ?

3. In ΔCDE, U is the centroid, and . Find each measure.

4. In ΔPQR, and is an altitude of ΔPQR. Find a. If is an angle bisector, find Find if is a median. If is a perpendicular bisector of find b.

is an altitude of ΔPQR. Find a. If is an angle bisector, find Find if is a median. If is a perpendicular bisector of find b.