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Pythagorean Theorem Warm-Up: Solving Right Triangles

Practice simplifying square roots and applying the Pythagorean Theorem to find missing sides of right triangles. Learn Pythagorean triples and classify triangles as right, acute, or obtuse. Solve for unknown side lengths and calculate triangle area.

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Pythagorean Theorem Warm-Up: Solving Right Triangles

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  1. Warm Up Simplify the square roots

  2. Sections 7.1-7.2 Pythagorean Theorem and its Converse Objective: To find missing sides of right triangles; to determine if a triangle is a right triangle.

  3. Pythagorean Theorem Where a and b are the legs of the right triangle and c is the hypotenuse. c a b

  4. 8 2.) 1.) x 15 17 36 y 225 Use the Pythagorean Theorem to solve for the variable. Write your answer in reduced radical form and decimal form. 82 + y2 = 172 152 + 362 = x2 64 + y2 = 289 225 + 1296 = x2 y2 = 225 1521 = x2 y = y = 15 39 = x

  5. Pythagorean Triple A set of three positive integers a, b, and c that satisfy the equation Pythagorean Triples: • 3, 4, 5 • 5, 12, 13 • 8, 15, 17 • 7, 24, 25 • And any multiple of the list above (p.435)

  6. The given lengths are two sides of a right triangle. All three sides of the triangle form a Pythagorean Triple. Find the length of the third side and tell whether it is a leg or hypotenuse. 1.) 40 and 41 2.) 12 and 35 3.) 63 and 65 122 = 144 632 = 3969 402 = 1600 352 = 1225 652 = 4225 412 = 1681 Sum is 1369, which is 372 Difference is 256, which is 162 Difference is 81, which is 92 Third side is 9. It’s a leg. Third side is 37. It’s a hypotenuse. Third side is 16. It’s a leg.

  7. Converse of Pythagorean Theorem : Right Triangle : Acute Triangle : Obtuse Triangle

  8. Decide whether the numbers represent the side lengths of a triangle. If they can, classify the triangles as right, acute, or obtuse. 1.) 20, 21, 28 2.) 15, 36, 39 3.) 14, 48, 50 20+21>28 21+28>20 20+28>21 15+36>39 36+39>15 15+39>36 14+48>50 48+50>14 14+50>48 282 ? 202 + 212 392 ? 152 + 362 502 ? 142 + 482 784 ? 400 + 441 1521 ? 225+1296 2500 ? 196+2304 784 < 841 1521 =1521 2500 =2500 acute right right

  9. Area of a triangle Area = ½ bh, where the base and height are perpendicular to each other. h h b b

  10. Find the area of the triangle given A = ½ bh 12 cm 10 ft. 7 ft. 8 cm 122 = a2 + 42 144 = a2 + 16 128 = a2 A = 35 ft2 A = 45.2 cm2 11.3 = a

  11. x 1.) 2.) x 2 2 = x2 + x Find the unknown side length. X2 + X2 = ( )2 2x2 = 64(2) 19 = x2 + 7 2x2 = 128 12 = x2 x2 = 64 x = x = 8

  12. Homework • Textbook pages 430-432 #3-25 every other odd • Textbook page 438 #3-25 every other odd

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