Lesson 3: Pythagoren Theorem
Duration of Days: 5
Lesson Objective
Students will explain a proof of the Pythagorean Theorem and its converse.
Students will apply the theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
How can we prove the relationship between the areas of the squares on the sides of a right triangle?
In what ways can the Pythagorean Theorem be used to solve for missing side lengths in 2D and 3D shapes?
How do we use the converse of the theorem to verify if a triangle is a "right" triangle?
Pythagorean Theorem, Leg, Hypotenuse, Right Triangle, Base, Square Root, Radical, and Converse
8.G.B.6: Explain a proof of the Pythagorean Theorem and its converse.
8.G.B.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Purpose: To transition students from finding areas of squares to generalizing the relationship between side lengths of right triangles.
Students use exploration and concrete models to construct mathematical arguments and solve practical problems.
DOK Level: 2 (Skill/Concept) and 3 (Strategic Thinking).
Confusing the legs (a and b) with the hypotenuse (c) when setting up the equation.
Thinking the theorem applies to any triangle rather than strictly right triangles.
Anchor charts
Hands-on activities
Exit tickets
Student work