honors geometry section 5 4 the pythagorean theorem
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Honors Geometry Section 5.4 The Pythagorean Theorem

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Honors Geometry Section 5.4 The Pythagorean Theorem. In a right triangle the two sides that form the right angle are called the legs , while the side opposite the right angle is called the hypotenuse.

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Presentation Transcript
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In a right triangle the two sides that form the right angle are called the legs, while the side opposite the right angle is called the hypotenuse.

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Consider placing four congruent right triangles with legs a and band hypotenuse c as shown at the right. Notice that the large figure is a square. Using the formula for the area of a square (A = s2) what is its area?

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We can also find the area of the large figure by adding the areas of the smaller square and the four triangles. The area of a triangle is found by the formula .

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The Pythagorean TheoremFor any right triangle with hypotenuse c and legs a and b, the sum of the squares of the legs ( )is equal to the square of the hypotenuse ( ).

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Example: If a 25-foot ladder is leaning against a house and the bottom of the ladder is 9 feet away from the house, how far up the side of the house is the top of the ladder? Round to the nearest 1000th.

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The converse of the Pythagorean Theorem is also true.Pythagorean Theorem ConverseIf the square of the largest side of a triangle equals the sum of the squares of the other two sides, then the triangle is a right triangle.

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Examples: Is a triangle with the given sides acute, right, obtuse or can’t exist. If the triangle cannot exist, explain why.
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Examples: Is a triangle with the given sides acute, right, obtuse or can’t exist. If the triangle cannot exist, explain why.
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