Tuesday, December 12, 2006
Geometry (Class 35)
Overview
§5.3 Medians and Altitudes of a Triangle
Today we learn how to construct the three altitudes of a triangle. We then use our constructions to calculate the areas of various triangles and discover (realize) something surprising.
Key Attitudes
Mathematics can be a tool for investigating and uncovering facts.
Knowing what to measure and how to measure it makes a complicated world much less so.
Investigating requires creativity and persistence.
If you don’t first succeed, try, try again.
Key Ideas
An altitude of a triangle is constructed by creating a perpendicular segment connecting a vertex to the side opposite the vertex.
Every triangle has three altitudes.
Sometimes altitudes are inside, sometimes they are outside, and sometimes they are on the triangle.
Key Skills
Constructing a perpendicular line passing through a point not on the line.
Constructing the orthocenter of a triangle.
Plotting points on a coordinate graph.
Vocabulary
altitude of a triangle
line that contains a side
Assignment
Balance a Triangle Part 4: Concurrency of the Medians of a Triangle (will be graded). Due Monday 12/18. This assignment is worth 200 points. (Extra points if turned in at the start of class Thursday 12/14).
Chapter 5 Review: Part 1, page 1. The whole assignment (pages 1-4) will be worth 300 points.
Quiz 5 Corrections
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