Isosceles triangle construction given base and altitude with compass and straightedge or ruler

Constructing an Isosceles Triangle (given base and altitude)

- Printable problem worksheet
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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

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

Try it yourself

Click here for a printable isosceles construction worksheet containing two problems to try. When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.

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