Constructing the altitude of an acute triangle

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See also the animated version.

After doing this Your work should look like this

We start with an acute triangle PQR.
See also the version for obtuse triangles.

1.  Choose one side of the triangle and extend it in both directions.
This is done because the side may not be long enough to perform the steps that follow.

In steps 2 through 5 which follow, we are constructing the perpendicular to the line PQ through R. This is is the same construction as Constructing a perpendicular to a line through an external point.
2.  Set the compass on the opposite vertex (here R) and set the width to beyond the line PQ.
3.  Make two arcs across PQ, creating the points A and B.
4.  From A and B, make two arcs that overlap, creating point C. Make sure both arcs are drawn with the same compass width.
5.  Draw a line through R and C. Label the point S where it crosses PQ.

Done   The segment RS is an altitude of the triangle PQR.

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Other constructions pages on this site




Right triangles

Triangle Centers

Circles, Arcs and Ellipses


Non-Euclidean constructions