To discover the Pythagorean Theorem by exploring right triangles and the squares built on each side To apply the Pythagorean Theorem to real-world problems.

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Presentation transcript:

To discover the Pythagorean Theorem by exploring right triangles and the squares built on each side To apply the Pythagorean Theorem to real-world problems

Add the two diagonals to the two small squares on the first picture on the Discovering the Pythagorean Theorem Template

Will the area of the two small squares fit inside the largest square? Try to duplicate the 8 triangular shapes in the largest square. What does this show you about the area of the two smaller squares and the area of the largest square?

Rearrange the four right triangles and the small square in the large square. What does this show you about the area of the two smaller squares and the area of the largest square?

Suppose that each leg in triangle 1 was 1. Use the area to find the length of the hypotenuse. Triangle 1 Triangle 2 1 1

Suppose that each leg in triangle 1 was 2. Use the area to find the length of the hypotenuse. Triangle 1 Triangle 2 2 2

Suppose that each leg in triangle 1 was 3. Use the area to find the length of the hypotenuse. Triangle 1 Triangle 2 5 5

Suppose that the hypotenuse of triangle 2 was 2 and the short leg was 1. Use the area to find the length of the longer leg. Triangle 1 Triangle 2 2 1

Suppose that the hypotenuse of triangle 2 was 4 and the short leg was 2. Use the area to find the length of the longer leg. Triangle 1 Triangle 2 4 2

Suppose that the hypotenuse of triangle 2 was 6 and the short leg was 3. Use the area to find the length of the longer leg. Triangle 1 Triangle 2 6 3

Place the Pythagorean Theorem Template in your communicator. Let a and b represent the lengths of the two legs and c be the length of the hypotenuse. Use the area of the squares to find the missing sides: a=3, b=4 b=8, c=10 a=5, c=13 a=7, b=24 b=15, c=17 b=24, c=26 a=12, b=35