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GeoGebraClasse GeoGebra
GeoGebra

Pythagorean Theorem Extension Discovery

Auteur :Jillian Korpi, Karen Campe, Dr. Edgar, Harmony Richman, Steve Phelps
We have been talking about the Pythagorean Theorem. Today, we will do a little exploration on the Converse of the Pythagorean Theorem. Answer the questions in this activity to gain a better insight into all that the Pythagorean Theorem can help us do!

Let's Challenge!

What do you notice about the area of the red shape compared to the area of the blue and green? Is your observation true for each red shape?

Did your observation from above hold when looking at the irregular shapes? State your conclusion below.

Design a shape above, and see if the sum of the area of the legs add to be the area of the hypotenuse. If you can find a shape that does not hold true, how far off is it? Could it be an error due to rounding?

Let's Back Up for a Few Review Questions

What is the formula for the Pythagorean Theorem?

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From your equation, which variable represents the hypotenuse?

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  • A
  • B
  • C
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If the sides of a right triangle are not labeled, how do you know which side is the hypotenuse? The hypotenuse is always the ________________ side.

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What is a triangle called if all of the angle measures are less than ?

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  • A
  • B
  • C
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If right triangles have the relationship of , what do you predict the relationship is between the side lengths of acute or obtuse triangles?

Let's Find Out!

Grab and move one of the large blue points to change the triangle.

Be sure the largest side is the one with the RED measurement!
  1. Create 6 triangles: 2 acute, 2 right, and 2 obtuse.
  2. Enter the side measurements into a chart like the one below.
  3. Calculate A2 + B2 and C2.
  4. Create different triangles to complete the chart.

Record data in this chart.

Do any of your triangles meet the requirements of the Pythagorean Theorem?

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What do you notice about the triangles where c2 < a2 + b2 ?

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What do you notice about the triangles where c2 > a2 + b2 ?

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Let's Practice

I have a sandwich cut into triangles. The side lengths of my triangular sandwich chunk are 3 inches, 4.5 inches, and 6 inches. What type of triangle is my sandwich? How do you know?

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I now have a piece of pizza with side lengths of 3.5 inches, 5.8 inches, and 6.1 inches. Is my pizza a right triangle? If not, what kind is it? How do you know?

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Go back to the editable triangle (the "Let's Find Out" section) and make the triangle sandwich then the pizza. Were you correct in labeling the kind of triangles I had? If not, adjust your answers and reasoning.

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