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Geometry 5.7

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The Pythagorean Theorem

- Students will be able to…
- Use the Pythagorean theorem and its converse to solve problems.
- Use Pythagorean inequalities to classify triangles.

c

a

b

Hypotenuse – Always the longest side.

- Side opposite the right angle.

- Side c is the hypotenuse

Pythagorean Theorem:

c

a

b

Leg – The two shorter sides.

- The sides that make up the right angle.

- a and b are the legs

Find the value of x

Find the value of x

- Pythagorean Triples – all sides of the right triangle are whole numbers.
- Still use the Pythagorean theorem to find the missing side.
- However, when done if you notice that all three numbers are whole numbers then you have a Pythagorean triple.
- 3, 4, 5 is a Pythagorean triple and any number times 3, 4, and 5 will create a Pythagorean triple.

- Find the missing side. Tell if the side lengths form a Pythagorean Triple

Find the missing side. Tell if the side lengths form a Pythagorean Triple

- Tell if the measures can be the side lengths of a triangle. If so classify the triangle.
- Step 1: Determine if a triangle
- Step 2: Classify the triangle
- Classify the triangle using the following chart

- Tell if the measures can be the side lengths of a triangle. If so classify the triangle.
- A. 8, 11, 13B. 7, 12, 16

- Tell if the measures can be the side lengths of a triangle. If so classify the triangle.
- C. 5.8, 9.3, 15.6D. 3.8, 4.1, 5.2

- Tell if the measures can be the side lengths of a triangle. If so classify the triangle.
- E. 5, 7, 10F. 11, 18, 34