8.1 Pythagorean Theorem Inequalities.notebook · 8.1 Pythagorean Theorem Inequalities.notebook 8...

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8.1 Pythagorean Theorem Inequalities.notebook 1 October 01, 2018 A B C Warm Up:

Transcript of 8.1 Pythagorean Theorem Inequalities.notebook · 8.1 Pythagorean Theorem Inequalities.notebook 8...

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A

B

C

Warm Up: 

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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.

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8.1 Pythagorean Theorem and Its Converse

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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.

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Solve for x:

13.2

7 x

13.2

7x

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Theorem 8­2 gs

Converse of the Pythagorean TheoremIf 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.

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We know that for a right triangle: 

Or if Pythagorean Theorem is true then:

it's a right triangle!

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Theorem 8­3If 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

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What if c2 > a2 + b2

Obtuse!

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Theorem 8­4If 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

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What if c2 < a2 + b2

Acute!

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SummaryIF 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

you have an obtuse triangle  c2 > a2 + b2

 c2 < a2 + b2 you have an acute triangle

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Examples

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Examples

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ExamplesClassify a triangle with side lengths           .

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Can you come up with another one???

Pythagorean Triple

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

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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.

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4-8 The Pythagorean Theorem 0806.4.1 Use and apply the Pythagorean Theorem to solve contextual problems The Pythagorean Theorem.

4-8 The Pythagorean Theorem 0806.4.1 Use and apply the Pythagorean Theorem to solve contextual problems The Pythagorean Theorem.

Pythagorean Theorem Inequality and Pythagorean Triples

Pythagorean Theorem Inequality and Pythagorean Triples

10.1 Pythagorean Theorem

10.1 Pythagorean Theorem

Big and Small - CUSD 4...Proving the Pythagorean Theorem Proving the Pythagorean Theorem and the Converse of the Pythagorean Theorem 1. Use this figure to prove the Pythagorean Theorem.

Big and Small - CUSD 4...Proving the Pythagorean Theorem Proving the Pythagorean Theorem and the Converse of the Pythagorean Theorem 1. Use this figure to prove the Pythagorean Theorem.

703 Pythagorean Theorem — Day 1 Essential Question: VOCAB Pythagorean Theorem… · 2020-02-10 · 703 Pythagorean Theorem — Day 1 Essential Question: VOCAB Pythagorean Theorem:

703 Pythagorean Theorem — Day 1 Essential Question: VOCAB Pythagorean Theorem… · 2020-02-10 · 703 Pythagorean Theorem — Day 1 Essential Question: VOCAB Pythagorean Theorem:

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Pythagorean Theorem

Proof pythagorean theorem

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The Pythagorean Theorem and Its Converse. Use the Pythagorean Theorem Use the Converse of the Pythagorean Theorem.

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Pythagorean Theorem Tutorial

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11.2 Pythagorean Theorem

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Pythagorean Theorem 170720 - josmfs.netjosmfs.net/.../2018/12/Pythagorean-Theorem-170720.pdf · Pythagorean Theorem 170720.doc 1 The Pythagorean Theorem 27 March 2016, rev 28 December

Pythagorean Theorem 170720 - josmfs.netjosmfs.net/.../2018/12/Pythagorean-Theorem-170720.pdf · Pythagorean Theorem 170720.doc 1 The Pythagorean Theorem 27 March 2016, rev 28 December

Pythagorean theorem 11.4

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Pythagorean Theorem .

Pythagorean Theorem .

Prove pythagorean theorem

Prove pythagorean theorem

Demonstration of the Pythagorean Theorem · Pythagorean Theorem Mathematics ... Demonstration of the Pythagorean Theorem ... The"top"portion"of"the"map"shows"the"Pythagorean"Theorem"expressed"in"the"form"a2

Demonstration of the Pythagorean Theorem · Pythagorean Theorem Mathematics ... Demonstration of the Pythagorean Theorem ... The"top"portion"of"the"map"shows"the"Pythagorean"Theorem"expressed"in"the"form"a2

A Brief History of the Pythagorean Theorem · A Brief History of the Pythagorean Theorem ... 8.2 - The Pythagorean Theorem and its Converse a2 + b2 = c2 The Pythagorean Theorem: ...

A Brief History of the Pythagorean Theorem · A Brief History of the Pythagorean Theorem ... 8.2 - The Pythagorean Theorem and its Converse a2 + b2 = c2 The Pythagorean Theorem: ...

Pythagorean Theorem 5.4. Learn the Pythagorean Theorem. Define Pythagorean triple. Learn the Pythagorean Inequality. Solve problems with the Pythagorean.

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5-3A The Pythagorean Theorem You used the Pythagorean Theorem to develop the Distance Formula. Use the Pythagorean Theorem. Use the Converse of the Pythagorean.

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