Unit 8, Lesson 10
The Converse
Grade 8
Preparation
Lesson Narrative
This lesson guides students through a proof of the converse of the Pythagorean Theorem. Students then use the converse to decide whether a triangle with three given side lengths is a right triangle or not.
To understand the proof of the converse of the Pythagorean Theorem, students first consider the hands of a clock. As one hand rotates away from the other, the angle created between the two hands increases, as does the distance between the tips of each hand. This idea is carried over into the next activity where students are guided through a proof of the converse, which says that if , then the side lengths , , and must form a right triangle. In the last activity, students use this thinking around the structure of a right triangle to take a non-right triangle and determine how one of the sides can be changed to make it a right triangle (MP7).
- Determine whether a triangle with given side lengths is a right triangle using the converse of the Pythagorean Theorem.
- Generalize (orally) that if the side lengths of a triangle satisfy the equation $a^2+b^2=c^2$, then the triangle must be a right triangle.
- Justify (orally) that a triangle with side lengths 3, 4, and 5 must be a right triangle.
Let’s figure out if a triangle is a right triangle.
Required Preparation
None