Every profession has particular tools that they use all the time, a chef has their knives, the sewer a machine and the mathematician, well they have their construction tools.
No, not hammers and hard hats - Mathematicians use a compass, pencil and a straight edge.
From just these three things we can create (nearly) all of what we require in geometry.
Notice how I used the word straight edge and not ruler. Well that's because all we really need for the constructions is a straight edge, we often don't even need numbers!
A great Greek mathematician named Euclid, who is credited to have written the first mathematics textbook over 2000 years ago, went to great lengths to detail many of the mathematical constructions we will look at today. Geometrical constructions were so important to mathematics at the time because most problems were solved graphically, not arithmetically.
To construct congruent line segments with a compass and straightedge, follow the instructions below. Play and pause the video at each step to help you.
As we have seen, congruent means same, so congruent angles are 2 (or more) angles that are exactly the same size. They can be facing in any direction, but if they are the same size then the angles are congruent. You can think of congruent angles as copies of each other.
To construct congruent angles you need a compass and a straight edge.
Draw (freehand, with ruler and protractor, and with technology) two-dimensional geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.