Geometry

1. Geometry Chapter 5 Lesson 4 Use Medians and Altitudes

2. Learning Target • We will use medians and altitudes of triangles.

3. Medians and Altitudes • Median: A segment that goes from each point (vertex) of the triangle to the midpoint of the opposite side. • Every triangle has three medians. • Centroid: The point of concurrency of the medians of a triangle. ( where all three medians meet)

4. Medians and Altitudes (cont’d) • Centroid Theorem: The centroid of a triangle is two thirds of the distance from each vertex to the midpoint of the opposite side. • If M is the centroid of ∆ABC, AM = 2/3 AE, BM = 2/3 BC, and FM = 2/3 FD B D E M centroid A C F

5. B D E M A C F

15. Using Centroid Theorem • For extra help on this topic: • Look at example 1 on page 319 • Look at example 2 on page 320 Lets try: • Guided practice #1-3 on page 320 in the middle of the page.

17. Medians and Altitudes (cont’d) • Altitude: A segment joining the vertex of a triangle to the line containing the opposite side at 90°. • Every triangle has three altitudes. • Draw pictures

18. Theorem 5.9 • Just something to know: You do not have to draw or write this: • Concurrency of Altitudes of a triangle: The lines containing the altitudes are concurrent ( meet at a point)

19. Orthocenter: The point of concurrency of the altitudes of a triangle. • Acute triangle the orthocenter is on inside of a triangle. • Right triangle the orthocenter is on the triangle. • Obtuse the orthocenter is on outside of triangle.

20. Medians and Altitudes (cont’d) • Find x and m 2 if MS is an altitude of ∆MNQ, m 1 = 3x + 11 and m 2 = 7x + 9. M R Q 2 1 S N m 2 = 58° 3x +11 + 7x + 9 = 90 10x + 20 = 90 10x = 70 x = 7

21. Together let’s try: • Page 322-323 # 3,5,7,9,13,15,17,21,25,35

22. Class work:: Assignment #3to be finished at home if you do not complete it here!! • Page 322-323 # 4, 6, 8, 10, 14, 16, 18, 19, 20, 24, 26, 27, 33, 34 • Page 325 46-55