Chapter 5 Section 4 Medians and Altitudes

Chapter 5 Section 4Medians and Altitudes

Objectives Students will be able to identify

properties of medians and altitudes in triangles

Essential Understanding A triangle’s three medians are always

concurrent The altitude of a triangle are

concurrent

Median of a Triangle Segment whose endpoints are a

vertex and the midpoint of the opposite side

Concurrency of Medians Theorem

Centriod of the Triangle Point of Concurrency of the medians

of a triangle Also called the center of gravity of a

triangle This is the point where the triangle

will balance Always inside the triangle Show on sketchpad

Finding the Length of a Median

ZA = 9, what is the length of ZC? What is the ration of ZA to AC?

Explain.

Altitude of a Triangle The perpendicular segment from the

vertex of the triangle to the line containing the opposite side

Can be on the inside, the outside, or a side of a triangle

Concurrency of Altitudes Theorem

The lines that contain the altitudes of a triangle are concurrent

The point of concurrency is called the orthocenter

sketchpad

Finding the Orthocenter Find the equations of two altitudes Then solve the system of equations ΔDEF has vertices D(1, 2), E(1, 6),

F(4, 2). What are the coordinates of the orthocenter of ΔDEF?

Summary

Homework Pg. 312 # 8 – 21, 24 – 27 18 problems