How to Construct a Triangle when Its Three Sides Are Given (SSS Criterion)

Say you need to construct a triangle having side lengths 6 centimeter (2.4 in), 7 centimeter (2.8 in) and 4 centimeter (1.6 in).

Draw a line segment measuring one of the given side lengths of the triangle. Let's draw the side having length 6 centimeter (2.4 in) and mark its end points as A and B. Use a ruler to carry out this step.

Set the width of your compass equal to another given side length. Let's set it equal to 7 centimeter (2.8 in). Retain this width for the next step.

Place the tip of the compass on one of the end points of the side AB (let's choose to place it on A) and draw an arc on either side of the line segment AB.

Set the width of your compass equal to length of the third side, which is 4 centimeter (1.6 in) in this case. Retain this width for the next step.

Place the tip of the compass on B and draw another arc which cuts the previously drawn arc at some point (say C).

Join C to each of the points A and B to complete the triangle. Triangle ABC conforms to the specified dimensions. AB = 6 centimeter (2.4 in), BC = 4 centimeter (1.6 in), CA = 7cmErase any extraneous constructions if you so wish.Construct a Triangle when Its Three Sides Are Given (SSS Criterion) Step 6Bullet1.jpg