The orthocenter of a triangle is a special point found where all three altitudes of the triangle intersect. An altitude is a line segment from a vertex of the triangle perpendicular to the opposite side (or the extension of the opposite side). This worksheet will guide you through the process of constructing orthocenters using just a compass and straightedge, helping you visualize and understand this key geometric concept. Remember, practice makes perfect!
Match the term with its definition:
| Term | Definition |
|---|---|
| 1. Altitude | A. The point where the three altitudes of a triangle intersect. |
| 2. Perpendicular | B. A line segment from a vertex to the opposite side forming a right angle. |
| 3. Vertex | C. Forming a right angle (90 degrees). |
| 4. Orthocenter | D. A point where two or more line segments meet. |
| 5. Intersection | E. A corner point of a triangle. |
Answers: 1-B, 2-C, 3-E, 4-A, 5-D
The orthocenter of a triangle is the point of __________ of the three __________. An altitude is a line segment from a __________ of the triangle to the __________ side, forming a __________ angle. To find the orthocenter, you need to construct all three __________ and identify where they all __________.
Answers: intersection, altitudes, vertex, opposite, right, altitudes, intersect
Can the orthocenter of a triangle ever lie outside the triangle? If so, under what conditions?
Yes, the orthocenter of an obtuse triangle (a triangle with one angle greater than 90 degrees) lies outside the triangle.
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