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### Transcript of 8.1 Pythagorean Theorem 8.1 Pythagorean Theorem 8 October 01, 2018 Theorem 8آ­2 gs Converse of the...

• 8.1 Pythagorean Theorem Inequalities.notebook

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October 01, 2018

A

B

C

Warm Up:

• 8.1 Pythagorean Theorem Inequalities.notebook

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October 01, 2018

Learning Goal: Today I will learn how to  apply the Pythagorean theorem and its  converse to classify triangles.

Success Criteria: I am able to classify  triangles as acute, right or obtuse.

• 8.1 Pythagorean Theorem Inequalities.notebook

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October 01, 2018

8.1 Pythagorean Theorem and  Its Converse

• 8.1 Pythagorean Theorem Inequalities.notebook

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Theorem 8­1

Pythagorean Theorem

gs

If a triangle is a right triangle, then the sum of  the squares of the lengths of the legs is equal  to the square of the length of the hypotenuse.

• 8.1 Pythagorean Theorem Inequalities.notebook

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October 01, 2018

• 8.1 Pythagorean Theorem Inequalities.notebook

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October 01, 2018

• 8.1 Pythagorean Theorem Inequalities.notebook

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October 01, 2018

Solve for x:

13.2

7 x

13.2

7 x

• 8.1 Pythagorean Theorem Inequalities.notebook

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October 01, 2018

Theorem 8­2 gs

Converse of the Pythagorean Theorem If the sum of the squares of the lengths of two  sides of a triangle is equal to the square of the  length of the third side, then the triangle is a right  triangle.

• 8.1 Pythagorean Theorem Inequalities.notebook

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October 01, 2018

We know that for a right triangle:

Or if Pythagorean Theorem is true  then:

it's a right triangle!

• 8.1 Pythagorean Theorem Inequalities.notebook

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October 01, 2018

Theorem 8­3 If the square of the length of the longest side of  a triangle is greater than the sum of the  squares of the lengths of the other two sides,  then the triangle is obtuse.

gs

• 8.1 Pythagorean Theorem Inequalities.notebook

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October 01, 2018

What if c2 > a2 + b2

Obtuse!

• 8.1 Pythagorean Theorem Inequalities.notebook

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October 01, 2018

Theorem 8­4 If the square of the length of the longest side  of a triangle is less than the sum of the  squares of the lengths of the other two sides,  then the triangle is acute.

gs

• 8.1 Pythagorean Theorem Inequalities.notebook

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October 01, 2018

What if c2

• 8.1 Pythagorean Theorem Inequalities.notebook

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Summary IF THEN

you have a right triangle a2 + b2 = c2

c2 > a2 + b2 you have an obtuse triangle

a2 + b2 = c2 you have a right triangle

you have an acute triangle  c2  a2 + b2

c2

• 8.1 Pythagorean Theorem Inequalities.notebook

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October 01, 2018

Examples

• 8.1 Pythagorean Theorem Inequalities.notebook

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October 01, 2018

Examples

• 8.1 Pythagorean Theorem Inequalities.notebook

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October 01, 2018

Examples Classify a triangle with side lengths           .

• 8.1 Pythagorean Theorem Inequalities.notebook

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• 8.1 Pythagorean Theorem Inequalities.notebook

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October 01, 2018

Can you come up with another one???

Pythagorean Triple

• 8.1 Pythagorean Theorem Inequalities.notebook

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October 01, 2018

Closure: Today I learned how to apply the  Pythagorean Theorem and its converse to  classify triangles.

• 8.1 Pythagorean Theorem Inequalities.notebook

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1 2 3

4 5 6

7.  A square has side length 10ft.  What is the diagonal  length of the square?  Express in simplest radical form.

8.  A square has diagonal length 9m.  What is the side  length of the square?

9.  A repairman leans the top of an 8 ft ladder against the tip of a  stone wall.  The base of the ladder is 5.5 ft from the wall.  About  how tall is the wall?  Round to the nearest tenth of a foot.

• 8.1 Pythagorean Theorem Inequalities.notebook

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