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2.9 – Medians and Altitudes
- Explore the medians and altitudes of triangles.
- Discover the centroids, orthocenters, incenters, and circumcenters of triangles.
- Altitude of a Triangle – The line segment from a vertex of a triangle that is perpendicular to the opposite side.
- The altitude is sometimes OUTSIDE of the triangle
- The altitude is sometimes ON the triangle’s side (right triangles)
- Median of a triangle – A line or segment joining a vertex of a triangle to the midpoint of the opposite side.
- In the example below, the median passes through vertex A and bisects side .
- Orthocenter – The point at which the three altitudes of a triangle intersect.
- The othercenter is found (the purple dot in the image below):
- Inside acute triangles
- Outside obtuse triangles
- On the vertex of a the right angle for right triangles
- Centroid of a triangle – The point at which the three medians of a triangle intersect.
- The centroid of any triangle is ALWAYS INSIDE the triangle
- How to Find the Centroid of a Triangle:
- Step 1: Find the midpoint of one side.
- Step 2: Draw a segment connecting the midpoint to its opposite vertex.
- Step 3: Repeat steps 1 and 2 for the other two sides.
- Step 4: The point where the three segments intersect is the centroid
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