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Pythagorean theorem

Autor:Emily_Gabriel1

Instructions

This activity will introduce students to the Pythagorean theorem. They will explore the relationship between the side lengths of perfect squares and how they form right angles.
Image

Warm Up

Emily is at her apartment and needs to buy groceries at Trader Joe's as quick as possible. If point B represents Emily's apartment, should she take route 66 to get to Trader Joe's? Or should Emily take Fern Avenue and turn right on Travers Place to get to Trader Joe's? What roads should Emily take and explain why you think so?

Record your wonders and observations about the right triangle below.

Recall: Hypotenuse- the longest side of a right triangle. It is the side that is across from the right angle. Legs-the shortest sides of a right triangle. Pythagorean Theorem: A formula used to determine unknown lengths in a right triangle. But how do we find the formula?

You should have discovered the three rectangles used to make a perfect right triangle. Now, what does it mean that we are using squares? If the side lengths of each three squares are a, b, and c, respectively, how can we show the area of each square using mathematics?

Do the following lengths form a right triangle?

Can you form a right triangle?

Marca todas las que correspondan
  • A
  • B
Revisa tu respuesta (3)

Can you form a right triangle?

Marca todas las que correspondan
  • A
  • B
Revisa tu respuesta (3)
Using the squares below to form a right triangle.

Do you see any relationships between the areas of the three squares? Write down your thoughts.

Write your equation below!

Let's apply our equation to a real life scenario! In a right angled triangle, we have discovered the formula: a^{2}+b^{2}=c^{2}. Now, say you have just picked up a ground ball at first base, and you see the other team's player is running towards third base. How far do you have to throw the ball to get it from first base to third base to throw the runner out? [Assume units are in feet. Hint: Using the segment tool to create a line might help visualize what you need to find out.]

Write down your answer below and briefly explain your steps.

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