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7.2: The Pythagorean Theorem and Its Converse

7.2: The Pythagorean Theorem and Its Converse. Objective: The use the Pythagorean Theorem and its converse. All the squares below are made of gold. You have your choice of the larger pink one, or you can take the two smaller ones together. Which option would you choose?. PYTHAGOREAN THEOREM.

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7.2: The Pythagorean Theorem and Its Converse

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  1. 7.2: The Pythagorean Theorem and Its Converse Objective: The use the Pythagorean Theorem and its converse

  2. All the squares below are made of gold. You have your choice of the larger pink one, or you can take the two smaller ones together. Which option would you choose?

  3. PYTHAGOREAN THEOREM • MUST be used on a right triangle • c is the hypotenuse, a and b are the legs of the right triangle a2 + b2 = c2

  4. Pythagorean Triple A set of nonzero, whole numbers a, b, and c that satisfy the Pythagorean theorem, a2 + b2= c2. Therefore, they represent the sides of a RIGHT TRIANGLE Common examples: 3, 4, 5 8,15,17 5,12,13 7,24,25

  5. Examples • a.) Find x. b.) Do the side lengths form a Pythagorean Triple? • Find x. 12 6 x 25 10 x

  6. Theorems: • If a2 + b2 = c2, the triangle is a right triangle. • If a2 + b2 < c2, the triangle is obtuse. • If a2 + b2 > c2, the triangle is acute.

  7. A triangle has the following side lengths. Is it a right triangle? • 16, 48,50 • 84, 85, 13

  8. Classify the triangles as obtuse, acute or right. • 6, 11 , 14 2. 15,25,20 3. 9, 8, 7

  9. Finding Area Find the area of the triangle. What do I need first? 7

  10. Find the area of the triangle. The isosceles triangle can be split into 2 right triangles. Use this to find h, which is the height of the whole triangle. 12 m 12 m h 20 m

  11. A 48-inch wide screen television means that the measure along the diagonal is 48 inches. If the screen is a square, what are the dimensions of the length and the width? Round your answers to the nearest hundredth.

  12. A baseball diamond is a square with 90 ft sides. Home plate and second base are opposite vertices of the square. About how far is home plate from second base?

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