Problem 1 Finding the Length of a Median
GRIDDED RESPONSE
In the diagram below,
Plan
How do you use the centroid?
Write an equation relating the length of the whole median to the length of the segment from the vertex to the centroid.
A is the centroid of
✓ Got It?
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- In the diagram for Problem 1,
- Reasoning What is the ratio of ZA to AC? Explain.
- In the diagram for Problem 1,
An altitude of a triangle is the perpendicular segment from a vertex of the triangle to the line containing the opposite side. An altitude of a triangle can be inside or outside the triangle, or it can be a side of the triangle.
Problem 2 Identifying Medians and Altitudes
Plan
How do you determine whether a segment is an altitude or a median?
Look at whether the segment is perpendicular to a side (altitude) and/or bisects a side (median).
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For
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For
✓ Got It?
- For
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Take Note Theorem 5-9: Concurrency of Altitudes Theorem
The lines that contain the altitudes of a triangle are concurrent.
You will prove Theorem 5-9 in Lesson 6-9.
Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs