Medians, and Altitudes.

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Presentation transcript:

Medians, and Altitudes

Objectives Identify and use medians and altitudes in ∆s

Medians A median is a segment whose endpoints are a vertex of a ∆ and the midpoint of the side opposite the vertex. Every ∆ has three medians. These medians intersect at a common point called the centroid. The centroid is the point of balance for a ∆.

Medians (continued) Theorem 5.7 (Centroid Theorem) The centroid of a ∆ is located two thirds of the distance from a vertex to the midpoint of the side opposite the vertex on a median.

Altitudes An altitude of a ∆ is a segment from a vertex to the line containing the opposite side and ┴ to the line containing that side. Every ∆ has three altitudes. The intersection point of the altitudes of a ∆ is called the orthocenter.

Altitudes (continued) Orthocenter

Example 1: ALGEBRA: Points U, V, and W are the midpoints of respectively. Find a, b, and c.

Example 1: Find a. Segment Addition Postulate Centroid Theorem Substitution Multiply each side by 3 and simplify. Subtract 14.8 from each side. Divide each side by 4.

Example 1: Find b. Segment Addition Postulate Centroid Theorem Substitution Multiply each side by 3 and simplify. Subtract 6b from each side. Subtract 6 from each side. Divide each side by 3.

Example 1: Find c. Segment Addition Postulate Centroid Theorem Substitution Multiply each side by 3 and simplify. Subtract 30.4 from each side. Divide each side by 10. Answer:

Your Turn: ALGEBRA: Points T, H, and G are the midpoints of respectively. Find w, x, and y. Answer: