Constructing Triangles

Starting with a sketch helps you see what information you already know and decide where to begin the construction. The sketch acts as a quick map of the triangle, so you can plan which side to draw first and which angles or arcs to construct next.

You cannot draw an angle on its own, because an angle needs two rays meeting at a point. By drawing a side first, you fix two vertices on the page. The given angle can then be constructed at one of those vertices, using the side as one of its arms.

This happens when you are given two sides and an angle that is not between them. When you draw the arc to locate the missing vertex, it can intersect the angle's ray at two different points. Each intersection produces a valid triangle from the same starting measurements.

When you draw arcs from both ends of the base, they meet at two points, one above the base and one below. Using the top intersection gives you the triangle in the correct orientation. The bottom intersection produces a different triangle with its vertices in a different anticlockwise order.

Use a protractor to measure and draw angles, since it shows degrees directly. Use a compass to mark out a length along a ray, or to draw arcs that locate a vertex from a known distance. Most triangle constructions use both tools together.