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8.1 Pythagorean Theorem Inequalities.notebook
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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.
8.1 Pythagorean Theorem Inequalities.notebook
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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.
8.1 Pythagorean Theorem Inequalities.notebook
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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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October 01, 2018
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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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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