1. 5.3 Concurrent Lines, Medians, and Altitudes Stand 0_23456789 Can you figure out the puzzle below??? No one understands!

2. Definitions Concurrent Lines: Three or more lines that meet at one point. Point of Concurrency: The point at which concurrent lines meet. l m n P k

3. Properties of Bisectors Theorem 5-6: The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices. Circumcenter of the Triangle: The point of concurrency of the perpendicular bisectors of a triangle.

4. Properties of Bisectors Theorem 5-7: The bisectors of the angles of a triangle are concurrent at a point equidistant from the sides. Incenter of the Triangle: The point of concurrency of the angle bisectors of a triangle.

5. Definitions Altitude of a Triangle: Perpendicular segment from a vertex to the line containing the opposite side. Median of a Triangle: A segments whose endpoints are a vertex and the midpoint of the opposite side.

6. Properties of Medians Centroid of a Triangle: The point of concurrency of the medians of a triangle. Theorem 5-8: The medians of a triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite sides.

7. Properties of Medians In the figure below, DE = 6 and AD = 16. Find DB and AF. F

8. Properties of Altitudes Orthocenter of a Triangle: The point of concurrency of the lines containing the altitudes of a triangle. Theorem 5-9: The lines that contain the altitudes of a triangle are concurrent.

9. Sum It Up Figureconcurrent at.. which is… bisector circumcenter incenter centroid orthocenter median bisector altitude equidistant from vertices equidistant from sides 2/3 distance from vertices to midpoint ---------------------

10. 5.3 Concurrent Lines, Medians, and Altitudes HW 5.3: #8-9, 11-16, 19-22, 28 KNEE LIGHT Can you figure out the puzzle below??? Neon Lights