1. 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.

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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.