Middle Grades Math: What's Right about Triangles

Objectives

• Students will explore how the area of a parallelogram remains unchanged if the base and height remain fixed while the side length changes.

Vocabulary

• right triangles
• hypotenuse and legs of a right triangle
• Pythagorean Theorem
• converse of a theorem
• area and perimeter
• parallelogram
• base and height

About the Lesson

This lesson involves examining a visual proof of the Pythagorean Theorem and supporting what happens geometrically.
As a result, students will:

• Explore the invariability of the areas of parallelograms that keep their base and height fixed but have different side lengths. This understanding will help students support what is happening with the visual proof the Pythagorean Theorem.
• Examine what kind of triangles have the sum of the squares of their shorter sides equal to the square of their largest side in order to explore the converse of the theorem.