Constructing a triangle given three sides (SSS)

After doing this	Your work should look like this
Start with three line segments that will be the three sides of the triangle ABC.
1.  Mark a point A that will be one vertex of the new triangle.
2.  Set the compasses' width to the length of the segment AB. This will become the base of the new triangle.
3.  With the compasses' point on A, make an arc near the future vertex B of the triangle.
4.  Mark a point B on this arc. This will become the next vertex of the new triangle.
5.  Set the compasses' width to the length of the line segment AC.
6.  Place the compasses' 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.
7.  Use the compasses to measure the length of the segment BC, the length of the third side of the triangle.
8.  From point B, draw an arc crossing the first. Where these intersect is the vertex C of the triangle
9.  Finally, draw the three sides AB, AC, and BC of the new triangle.
10.  Done. The blue triangle ABC has each side congruent to the the corresponding line segment.

Other constructions pages on this site

• List of printable constructions worksheets

Lines

• Introduction to constructions
• Copy a line segment
• Sum of n line segments
• Difference of two line segments
• Perpendicular bisector of a line segment
• Perpendicular at a point on a line
• Perpendicular from a line through a point
• Perpendicular from endpoint of a ray
• Divide a segment into n equal parts
• Parallel line through a point (angle copy)
• Parallel line through a point (rhombus)
• Parallel line through a point (translation)

Angles

• Bisecting an angle
• Copy an angle
• Construct a 30° angle
• Construct a 45° angle
• Construct a 60° angle
• Construct a 90° angle (right angle)
• Sum of n angles
• Difference of two angles
• Supplementary angle
• Complementary angle
• Constructing  75°  105°  120°  135°  150° angles and more

Triangles

• Copy a triangle
• Isosceles triangle, given base and side
• Isosceles triangle, given base and altitude
• Isosceles triangle, given leg and apex angle
• Equilateral triangle
• 30-60-90 triangle, given the hypotenuse
• Triangle, given 3 sides (sss)
• Triangle, given one side and adjacent angles (asa)
• Triangle, given two angles and non-included side (aas)
• Triangle, given two sides and included angle (sas)
• Triangle medians
• Triangle midsegment
• Triangle altitude
• Triangle altitude (outside case)

Right triangles

• Right Triangle, given one leg and hypotenuse (HL)
• Right Triangle, given both legs (LL)
• Right Triangle, given hypotenuse and one angle (HA)
• Right Triangle, given one leg and one angle (LA)

Triangle Centers

• Triangle incenter
• Triangle circumcenter
• Triangle orthocenter
• Triangle centroid

Circles, Arcs and Ellipses

• Finding the center of a circle
• Circle given 3 points
• Tangent at a point on the circle
• Tangents through an external point
• Tangents to two circles (external)
• Tangents to two circles (internal)
• Incircle of a triangle
• Focus points of a given ellipse
• Circumcircle of a triangle

Polygons

• Square given one side
• Square inscribed in a circle
• Hexagon given one side
• Hexagon inscribed in a given circle
• Pentagon inscribed in a given circle

Non-Euclidean constructions

• Construct an ellipse with string and pins
• Find the center of a circle with any right-angled object