Medians and Altitudes Median – A segment whose endpoints are a vertex of a triangle and the midpoint of the side opposite the vertex. Centroid – The point.

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Presentation transcript:

Medians and Altitudes Median – A segment whose endpoints are a vertex of a triangle and the midpoint of the side opposite the vertex. Centroid – The point of concurrency for the medians of a triangle. Centroid Theorem The centroid of a triangle is located two thirds of the distance from a vertex to the midpoint of the side opposite the vertex on a median.

ALGEBRA Points U, V, and W are the midpoints of. respectively ALGEBRA Points U, V, and W are the midpoints of respectively. Find a, b, and c. Example 1-2a

Segment Addition Postulate 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 1-2a

Segment Addition Postulate 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 1-2a

Segment Addition Postulate 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: Example 1-2a

ALGEBRA Points T, H, and G are the midpoints of. respectively ALGEBRA Points T, H, and G are the midpoints of respectively. Find w, x, and y. Answer: Example 1-2b

Medians and Altitudes Altitude - A segment from a vertex to the line containing the opposite side and perpendicular to the line containing that side. Orthocenter – The point of concurrency of the altitudes of a triangle.