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# Chapter 5 day 3

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### Chapter 5 day 3

1. 1. GT Geometry Drill 1/3/13• Pick up a piece of patty paper and draw a nice size triangle using your geometric tools• HW on the corner of your desk• Pass out papers in bin!• Midterm = 2 test grades
2. 2. 5-3 Medians and Altitudes of Triangles Objectives Apply properties of medians of a triangle. Apply properties of altitudes of a triangle.Holt McDougal Geometry
3. 3. 5-3 Medians and Altitudes of Triangles Vocabulary median of a triangle centroid of a triangle altitude of a triangle orthocenter of a triangleHolt McDougal Geometry
4. 4. 5-3 Medians and Altitudes of Triangles A median of a triangle is a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side. Every triangle has three medians, and the medians are concurrent.Holt McDougal Geometry
5. 5. 5-3 Medians and Altitudes of Triangles The point of concurrency of the medians of a triangle is the centroid of the triangle . The centroid is always inside the triangle. The centroid is also called the center of gravity because it is the point where a triangular region will balance.Holt McDougal Geometry
6. 6. 5-3 Medians and Altitudes of Triangles An altitude of a triangle is a perpendicular segment from a vertex to the line containing the opposite side. Every triangle has three altitudes. An altitude can be inside, outside, or on the triangle.Holt McDougal Geometry
7. 7. 5-3 Medians and Altitudes of Triangles In ΔQRS, altitude QY is inside the triangle, but RX and SZ are not. Notice that the lines containing the altitudes are concurrent at P. This point of concurrency is the orthocenter of the triangle.Holt McDougal Geometry
8. 8. 5-3 Medians and Altitudes of Triangles Helpful Hint The height of a triangle is the length of an altitude.Holt McDougal Geometry
9. 9. vocabulary The midsegment of atriangle - Segment thatjoins the midpoints of any two sides of a triangle.
10. 10. Triangle Midsegment
11. 11. TheoremThe midsegment of a triangle is half the length of, and parallel to, the third side of a triangle.