Standard: M8G2. Students will understand and use the Pythagorean theorem.a. Apply properties of right triangles, including the Pythagorean theorem.B. Recognize and interpret the Pythagorean theorem as a statement about areas of squares on the sides of a right triangle.

Essential Question:How can you use the Pythagorean theorem to determine whether a triangle is a right triangle based on the lengths of its sides.

How can we determine if this is a right triangle?

Measure to see if it has a right angle?

Can we use the Pythagorean theorem to check the side lengths? How?

Use the dot paper to create either an acute, obtuse, or right triangle that you like! The only requirement is that the side lengths must be 4 units, 3 units and 5 units.

Does your triangle look like this?

Does anyone has one that is different?

Is this a right triangle? How can we check?

Yes, let’s use the Pythagorean theorem.

a2 + b2 = c2

32 + 42 = 52

9 + 16 = 25

Yes, it satisfies the Pythagorean theorem. Hmmm?

Use the dot paper to create either an acute, obtuse, or right triangle that you like! The only requirement is that the side lengths must be 1 unit, 2 units and 2 units.

a2 + b2 = c2

12 + 22 = 22

1 + 4 = 4 5 = 4

I can’t seem to make a triangle using these lengths. Did any of you?

What happens when we use the Pythagorean theorem?

5 does NOT equal 4 so this CAN NOT be a right triangle?

Now complete your worksheet!

YES YES

YES YES

YES

NO NO

YES

NO NO

NO NO

B.1. If a triangle’s side lengths satisfy the relationship a2 + b2 = c2 the triangle IS a right triangle.

2. If a triangle’s side lengths DO NOT satisfy the relationship a2 + b2 = c2 the triangle IS NOT a right triangle.

C.1. Yes.

122 + 162 = 202

144 + 256 = 400

2. YES.

82 + 152 = 172

64 + 225 = 289

3. NO.

92 + 122 ≠ 162

81 + 144 ≠ 256 225 ≠ 256

D.

M, N, Q and R. The side lengths of these triangles satisfy the Pythagorean theorem.