Students will be able to
- replicate a proof of the Pythagorean theorem
- determine whether the relationship a2 + b2 = c2 holds for all triangles
Common Core State Standards: 8.G.B.6, 8.G.B.7, 8.G.B.8
Vocabulary: Pythagorean theorem, right triangle, leg, hypotenuse
Materials: Copier paper, construction paper, rulers, scissors, protractor
1. Watching the Video (5 minutes, whole class)
Begin the lesson by watching a video about the Pythagorean theorem. Explain why this theorem is so important and talk about some of the real-life applications it has, especially in construction and architecture. Emphasize that the theorem can only be used with right triangles.
2. Activity (15 minutes, individuals)
In this activity, students will replicate a proof of the Pythagorean theorem. Each student will need two pieces of copier paper, construction paper, a ruler, a protractor, and scissors.
Have each student draw a right triangle on one piece of the white copier paper. Students should measure the right angle of their triangle with the protractor. They should also measure the exact length of the triangle’s legs and hypotenuse. Label one leg a, one leg b, and the hypotenuse c.
Then, using the construction paper, have students create three squares that correspond to the a, b, and c lengths of their triangle. Cut out the squares, label them a2, b2, and c2, and place them next to the corresponding sides, as shown in the video.
Now have students try to fit the two smaller squares (a2 and b2) into the larger square (c2) to mimic the proof shown in the video. (Alternatively, they could cut c2 so it fits into a2 and b2.) Can they cut the squares in a way that helps them see that a2 + b2 = c2?
Now repeat the whole process with a different-sized right triangle. Although the dimensions are different, does the relationship a2 + b2 = c2 hold true?
Extension: If students finish early, have them try this same activity with a nonright triangle. What do they find? Does the relationship a2 + b2 = c2 work with other triangles?
3. Discussion (10 minutes, whole group)
Review the results of the experiment. Did the a2 + b2 = c2 relationship hold true for every right triangle? Or did the results vary with the size or shape of the triangle? Discuss students’ findings and their explanations about why they found what they did. (Students can also answer these questions in the form of an exit ticket.) Then, show some examples of how the Pythagorean theorem can be used to find the length of the hypotenuse in a right triangle in which the other two side lengths are known.
Pythagorean Theorem Worksheets
Working with the Pythagorean Theorem
Here is a graphic preview for all of the Pythagorean Theorem Worksheets. You can select different variables to customize these Pythagorean Theorem Worksheets for your needs. The Pythagorean Theorem Worksheets are randomly created and will never repeat so you have an endless supply of quality Pythagorean Theorem Worksheets to use in the classroom or at home. Our Pythagorean Theorem Worksheets are free to download, easy to use, and very flexible.
These Pythagorean Theorem Worksheets are a great resource for children in 6th Grade, 7th Grade, and 8th Grade.
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Pythagorean Theorem Practice Problems Worksheets
This Pythagorean Theorem Problems Worksheet will produce problems for practicing solving the lengths of right triangles. You may choose the type of numbers and the sides of the triangle. This worksheet is a great resources for the 6th Grade, 7th Grade, and 8th Grade.
Distance Formula Problems Worksheets
This Pythagorean Theorem Distance Problems Worksheet will produce problems for practicing solving distances between two sets of points on a coordinate plane. You may choose between single quadrant or four quadrant problems. This worksheet is a great resources for the 6th Grade, 7th Grade, and 8th Grade.
Pythagorean Theorem Definitions and Examples Worksheets
These Pythagorean Theorem Worksheets will produce colorful and visual pages that contain definitions and examples for the Pythagorean Theorem and the Distance Formula. These worksheets are great resources for the 6th Grade, 7th Grade, and 8th Grade.