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Orthocenter of a Triangle Construction
Click here for a printable triangle orthocenter worksheet
How to construct the
orthocenter of a
triangle.
We start with a given triangle ABC, and finish with a point indicating its orthocenter.
Instructions Click on 'Next' to go through the construction one step at a time, or click on 'Run' to let it run without stopping.
(If there is no image below, see support page.)
Step-by-step Instructions
| Step 1 |
Set the compass width to the length of a side of the triangle. Any side will do, but the shortest works best. |
| Step 2 |
With the compass on B, one end of that line, draw an arc across the opposite side. Label this point F |
| Step 3 |
Repeat for the other end of the line, C. Label this point P. |
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*Note If you find you cannot draw these arcs on the opposite sides, the orthocenter is outside the triangle. See note below* |
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What we do now is draw two altitudes. This is the same process as constructing a perpendicular to a line through a point. |
| Step 4 |
With the compass on B, set the compass width to about two thirds the distance to P. |
| Step 5 |
From B and P, draw two arcs that intersect, creating point Q. |
| Step 6 |
Use a straightedge to draw a line from C to Q. The part of this line inside the triangle forms an altitude of the triangle. |
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Now we repeat the process to create a second altitude. |
| Step 7 |
With the compass on C, set the compass width to about two thirds the distance to F. |
| Step 8 |
From C and F, draw two arcs that intersect, creating point E. |
| Step 9 |
Use a straightedge to draw a line from B to E. The part of this line inside the triangle forms an altitude of the triangle. |
| Step 10 |
Done. The point where the two altitudes intersect is the orthocenter of the triangle.
(You may need to extend the altitude lines so they intersect if the orthocenter is outside the triangle)
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*Note If you find you cannot draw the arcs in steps 2 and 3, the orthocenter lies outside the triangle. See
Orthocenter of a triangle
To solve the problem extend the opposite side until you can draw the arc across it. (See diagram right). Then proceed as usual.
Try it yourself
Click here for a printable worksheet containing two triangle orthocenter problems.
When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.
Other constructions
Lines
Angles
Triangles
Triangle Centers
Circles, Arcs and Ellipses
Non-Euclidean constructions
(C) 2007 Copyright John Page
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