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Pythagorean Theorem

Pythagorean Theorem. Problem Solving. The hypotenuse is the longest side of a right-angled triangle. 16. 25. 9. 625. 169. 49. 25. 576. 144.

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Pythagorean Theorem

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  1. Pythagorean Theorem Problem Solving

  2. The hypotenuse is the longest side of a right-angled triangle. 16 25 9 625 169 49 25 576 144 Draw squares on each side of the triangles below and record their areas in the table. The dots are to help you draw the large squares (next slide). What was it that Pythagoras discovered? The Theorem of Pythagoras 1 "In a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides”. 5 3 3,4,5 7,24,25 4 3 25 7 5,12,13 24 2 13 5 12

  3. 25 9 52= 32+ 42 16 25 = 9 + 16 A Pythagorean Triple In a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides. 3, 4, 5 5 3 4

  4. A 2nd Pythagorean Triple 5, 12, 13 169 25 132 = 52+ 122 144 169 = 25 + 144 In a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides. 13 5 12

  5. A 3rd Pythagorean Triple In a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides. 625 7, 24, 25 25 49 7 24 576 252= 72+ 242 625 = 49 + 576

  6. 1 x 3 cm 4 cm 2 x 5 cm 12 cm Pythagoras Questions

  7. 3 x 5 cm 6 cm 4 x 4.6 cm 9.8 cm Pythagoras Questions

  8. 5 11m x m 9 m 6 23.8 cm 11 cm x cm Pythagoras Questions

  9. 7 3.4 cm 7.1 cm x cm 8 x m 25 m 7 m Pythagoras Questions

  10. Applications of Pythagoras 1 Find the diagonal of the rectangle d 6 cm 9.3 cm 2 A rectangle has a width of 4.3 cm and a diagonal of 7.8 cm. Find its perimeter. 7.8 cm 4.3 cm x cm Perimeter = 2(6.5+4.3) = 21.6 cm

  11. 15 miles H B 6.4 miles L Applications of Pythagoras A boat sails due East from a Harbour (H), to a marker buoy (B), 15 miles away. At B the boat turns due South and sails for 6.4 miles to a Lighthouse (L). It then returns to harbour. Make a sketch of the journey. What is the total distance travelled by the boat? Total distance travelled = 21.4 + 16.3 = 37.7 miles

  12. 12 ft 9.5 ft L Applications of Pythagoras A 12 ft ladder rests against the side of a house. The top of the ladder is 9.5 ft from the floor. How far is the base of the ladder from the house?

  13. Find the diagonals of the kite 6 cm 5 cm 5 cm x cm y cm 12 cm

  14. a 3 b 7 Find the distance between two points, a and b with the given co-ordinates. a(3, 4) and b(-4, 1)

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