Chapter 5 Section 4 Medians and Altitudes
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Transcript of 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