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Honors Geometry Section 5.4 The Pythagorean Theorem

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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Honors Geometry Section 5.4 The Pythagorean Theorem

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  1. Honors Geometry Section 5.4The Pythagorean Theorem

  2. 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.

  3. 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?

  4. 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 .

  5. If we set the two expressions for the area of the larger square equal to each other, we get:

  6. 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 ( ).

  7. A Pythagorean Triple is three whole numbers that could be the sides of a right triangle.

  8. 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.

  9. 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.

  10. If a triangle is not a right triangle, then it must be either acute or obtuse.

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

  12. 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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