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Construct a triangle given three sides
Click here for a printable triangle construction worksheet

How to construct a a triangle when given the lengths of all three sides using only a compass and straightedge. We start with three segments that are the lengths of the three sides of the desired triangle. The result is the triangle ABC whose sides are congruent to the three segments.

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.)


Note: It is not always possible to construct a triangle from three given lines. See figure on the right. The two shortest sides must add to more than the longest side, or they will not link up to form a triangle. Se Triangle Inequality for more on this.
Step-by-step Instructions
Step 1 Mark a point A that will be one vertex of the new triangle.
Step 2 Set the compass width to the length of the segment AB. This will become the base of the new triangle.
Step 3 With the compass point on A, make an arc near the future vertex B of the triangle.
Step 4 Mark a point B on this arc. This will become the next vertex of the new triangle.
Step 5 Set the compass width to the length of the line segment AC.
Step 6 Place the compass point on A and make an arc in the vicinity of where the third vertex of the triangle (C) will be. All points along this arc are the distance AC from A, but we do not yet quite know exactly where the vertex C is.
Step 7 Use the compass to measure the length of the segment BC, the length of the third side of the triangle.
Step 8 From point B, draw an arc crossing the first. Where these intersect is the vertex C of the triangle
Step 9 Finally, draw the three sides of the new triangle AB, AC, and BC.
Step 10 Done. The blue triangle ABC has each side congruent to the the corresponding line segment.
Try it yourself
Click here for a printable worksheet containing two triangle construction problems where you are given the three side lengths. 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