Geometry Chapter 5 Lesson 4 Use Medians and Altitudes

Learning Target We will use medians and altitudes of triangles.

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)

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 Medians and Altitudes (cont’d) A F C B D E M centroid

A F C B D E M

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.

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

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)

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.

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 Q R M S N 3x x + 9 = 90 10x + 20 = 90 10x = 70 x = 7 m 2 = 58°

Together let’s try: Page # 3,5,7,9,13,15,17,21,25,35

Class work:: Assignment #3 to be finished at home if you do not complete it here!! Page # 4, 6, 8, 10, 14, 16, 18, 19, 20, 24, 26, 27, 33, 34 Page