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Medians and Altitudes
Medians and Altitudes
G.CO.10 Prove theorems about triangles... the medians of a triangle meet at a point.
Goals for this section:
Goals for this section:
Students should be able to identify a median and an altitude.
Medians
Medians
What is a median of a triangle?
What is a median of a triangle?
A median is a segment whose endpoints are a vertex and the midpoint of the opposite side.
Concurrency of Medians Theorem
Concurrency of Medians Theorem
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 side.
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 side.
Let's break that down:
Let's break that down:
- "The medians of a triangle are concurrent at a point..."
- This is looking at point P, where all the medians intersect and meet.
- "...that is two thirds the distance from each vertex to the midpoint of the opposite side."
- The distance from point P to a vertex is (2/3) the length of that corresponding median.
Centroid
Centroid
Point P is called a centroid! It is also called the "center of gravity" of a triangle because it is the point where a triangular shape will balance.
Altitudes
Altitudes
What is the altitude of a triangle?
What is the altitude of a triangle?
The altitude is a perpendicular segment from a vertex to the opposite side. Notice that it doesn't necessarily meet at the midpoint of the other side.
Altitudes can also be on the outside of the triangle or on the side of the triangle (a right triangles).
Practice
Practice
Identify whether the segment is an altitude, median, or neither.
- HK
- KM
- LI
Answers:
Answers:
- If AP = 12, then what is the length of AF?
- If DP = 2.4, find DB and PB.
- If CE = 18, then what is the length of CP?
Answers:
Answers:
Keywords: median, altitude, triangle
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