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

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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

    1

    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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    October 01, 2018

    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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    October 01, 2018

    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           .

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    October 01, 2018

  • 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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    October 01, 2018

    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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    October 01, 2018

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