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4 cards from this section. Quick, good the night before a test.
What is the orthocenter of a triangle?
Think about the altitudes and where they meet.
In which type of triangle is the orthocenter located at a vertex?
Consider the properties of right angles.
Where is the orthocenter located in an acute triangle?
Think about the angles of the triangle.
True or False: The orthocenter can be located outside the triangle in every type of triangle.
Review the definitions of acute, right, and obtuse triangles.
In triangle XYZ, with coordinates X(2, 3), Y(6, 3), and Z(4, 8), find the coordinates of the orthocenter by calculating the altitudes from each vertex.
Start by determining the slopes and equations of the lines formed by the triangle's vertices.
Demonstrate how the orthocenter's location affects the triangle's properties and provide a proof that in any triangle the orthocenter will always relate to the centroid and circumcenter on Euler's line.
Use coordinate geometry as a basis to establish proofs with calculated distances and angles.
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