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Constructing an isosceles triangle given base and altitude

This is the step-by-step, printable version. If you PRINT this page, any ads will not be printed.

See also the animated version.

After doing this Your work should look like this

We start with two line segments AB and CD that define the altitude and the base length of the triangle.

Geometry construction with compass and straightedge or ruler or ruler
1.  Draw a point P that will become one end of the base of the triangle. Geometry construction with compass and straightedge or ruler or ruler
2.  Place the point of the compasses on the point C and adjust the compasses' width to the desired length CD of the base of the finished triangle Geometry construction with compass and straightedge or ruler or ruler
3.  With the compasses' point on P, draw an arc. Geometry construction with compass and straightedge or ruler or ruler
4.  Pick a point R anywhere on the arc. This will become the other end of the base of the triangle. Geometry construction with compass and straightedge or ruler or ruler
5.  Draw the base line PR. Geometry construction with compass and straightedge or ruler or ruler
In the next three steps, we form the perpendicular bisctor of the base
6.  With the compasses' width set roughly to the base length (exact width is not important), draw an arc on each side of the base line from points P and R. Geometry construction with compass and straightedge or ruler or ruler
7.  Draw a line through the two arc intersections. This is the perpendicular bisector of the base, dividing it into two equal parts. Geometry construction with compass and straightedge or ruler or ruler
8.  Set the compasses' width to the distance from A to B. This is the desired altitude of the triangle. Geometry construction with compass and straightedge or ruler or ruler
9.  Place the point of the compasses on the midpoint of the base line, and draw an arc across the perpendicular drawn earlier. This is the third vertex of the triangle. Geometry construction with compass and straightedge or ruler or ruler
10.  Draw the two side lines PQ and RQ Geometry construction with compass and straightedge or ruler or ruler
11.  Done. The triangle PQR is an isosceles triangle. Geometry construction with compass and straightedge or ruler or ruler

Other constructions pages on this site

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Angles

Triangles

Right triangles

Triangle Centers

Circles, Arcs and Ellipses

Polygons

Non-Euclidean constructions