In this lesson, students explore what they can determine about a triangle when they have information about side lengths. They begin by playing with two known side lengths to understand that when two side lengths are the same, increasing the angle between them also lengthens the side opposite the angle. Then, students state the converse of the Pythagorean Theorem and use that to classify triangles as either acute, right, or obtuse based on the lengths of all three sides.

An optional activity is included to explore the idea that any side of a triangle must be less than the sum of the other two sides. 

Students must make use of the structure of triangles to determine what they can figure out about a triangle given a few of its side lengths (MP7).