1. Copyright © Ed2Net Learning, Inc. 11 Grade 8 Pythagorean Theorem #1

2. Copyright © Ed2Net Learning, Inc. 2 Pythagorean Theorem The Pythagorean Theorem shows how the legs and hypotenuse of a right triangle are related. legs hypotenuse In a right triangle, the two shortest sides are legs. The longest side, which is opposite the right angle, is the hypotenuse.

3. Copyright © Ed2Net Learning, Inc. 3 In words: In a right angled triangle, the square of the length of the hypotenuse is equal to the sum of the square of the lengths of the legs. In Symbols: a 2 +b 2 = c 2. a b c If we know the lengths of two sides of a right angled triangle, then Pythagoras' Theorem allows us to find the length of the third side. Pythagorean Theorem

4. Copyright © Ed2Net Learning, Inc. 4 hypotenuse = 2. shorter leg longer leg = shorter leg. √3 C 30º 60º 2s A B s √3s Using the Pythagorean theorem, we find that The converse of Pythagorean Theorem allows you to substitute the lengths of the sides of a triangle into the equation : c 2 = a 2 +b 2 to check whether a triangle is a right triangle, if the Pythagorean equation is true the triangle is a right triangle. 30-60-90 Triangle

5. Copyright © Ed2Net Learning, Inc. 5 Let us do some practice problems!

6. Copyright © Ed2Net Learning, Inc. 66 1) What are the angle measures of an isosceles right triangle? a)30°-90°-60° b)45°-90°-45° c)20°-90°-70° d)None of the above.

7. Copyright © Ed2Net Learning, Inc. 77 2) What is the relation between the length of the shortest side and hypotenuse in a 30 o - 60 o -90 o triangle? a)hypotenuse = 2. shorter leg b)hypotenuse = √3. shorter leg c)hypotenuse = 3. shorter leg d)None of the above.

8. Copyright © Ed2Net Learning, Inc. 88 3) One end of a wire of length 20 ft is tied to the top of the pole and the other end is fixed in the ground at a distance of 12 ft from the foot of the pole. What is the height of the pole? a)12 ft b)18 ft c)16 ft d)14 ft

9. Copyright © Ed2Net Learning, Inc. 99 4) The lengths of the perpendicular sides of a right angled triangle are 8 cm and 6 cm. Then find the perimeter of the triangle. a)18 cm b)20 cm c)22 cm d)24 cm

10. Copyright © Ed2Net Learning, Inc. 10 5) What is the value of b in the figure? a)24 ft b)24.25 ft c)24.50 ft d)24.75 ft 14 ft 30° 60° b

11. Copyright © Ed2Net Learning, Inc. 11 6) State whether the lengths 10, 11 and 15 are sides of a right triangle. a)True b)False

12. Copyright © Ed2Net Learning, Inc. 12 7) If c = 27 cm and b = 9 cm, then find the value of x in the right triangle. a)25.5 cm b)24.5 cm c)23.5 cm d)22.5 cm 9 cm 27 cmx

13. Copyright © Ed2Net Learning, Inc. 13 8) Bill walked diagonally across (from one corner to the opposite corner) a square garden with each side measuring 25 ft in length. How far did he walk? a)25√3 ft b)25√2 ft c)26√2 ft d)None of the above.

14. Copyright © Ed2Net Learning, Inc. 14 a)2√3 ft b)4√3 ft c)3√5 ft d)3√2 ft 9) What is the measure of the side of the square, if the diagonal of the square is 6 feet?

15. Copyright © Ed2Net Learning, Inc. 15 10) The length and the width of a rectangular field are 20 feet and 15 feet respectively. A diagonal walkway is made from one end to the opposite end. What is the length of the walkway? a)55 ft b)45 ft c)35 ft d)25 ft

16. Copyright © Ed2Net Learning, Inc. 16 Assessment

17. Copyright © Ed2Net Learning, Inc. 17 1) If one side of a right triangle is two times the other and the length of hypotenuse is 25 ft, then what are the measures of the two sides? a)4√5 ft; 8√5 ft b)5√5 ft; 10√5 ft c)7√5 ft; 14√5 ft d)6√5 ft; 12√5 ft

18. Copyright © Ed2Net Learning, Inc. 18 2) What is the length of the third side of the triangle shown in the figure? [Given a = 9.6 cm and b = 12.8 cm] 9.6 cm 12.8 cm x a)17 cm b)15 cm c)14 cm d)16 cm

19. Copyright © Ed2Net Learning, Inc. 19 3) What is the value of x? 30º 60º A B 7 cm x C a)12.7 cm b)11.7 cm c)12.1 cm d)11.5 cm

20. Copyright © Ed2Net Learning, Inc. 20 4) Sheath went to a level field to fly a kite. She let out all 195 ft of string and tied it to a stake. Then she walked out on the field until she was directly under the kite, 117 ft from the stake. How high was the kite? a)156 ft b)140 ft c)142 ft d)168 ft

21. Copyright © Ed2Net Learning, Inc. 21 5) If b = 20.4 units and c = 25.5 units, then find the value of a in a right triangle. a)17.3 units b)16.6 units c)15.3 units d)18.5 units

22. Copyright © Ed2Net Learning, Inc. 22 6) The hypotenuse of a right triangle is 40 meters long, and one of its leg is 18 meters long. Find the length of the other leg. a)32.3 m b)35.7 m c)36.2 m d)36.5 m

23. Copyright © Ed2Net Learning, Inc. 23 7) A ramp used in skateboarding competitions is shown below. How high is the ramp? a)12.3 m b)14.2 m c)12.7 m d)13.2 m 20 m 15 m

24. Copyright © Ed2Net Learning, Inc. 24 8) What is the length of the diagonal of a square if its area is 64 m 2 ? a)7√2 m b)8√2 m c)8√3 m d)8√5 m

25. Copyright © Ed2Net Learning, Inc. 25 9) The perimeter of a right triangle is 60 cm and the sum of the squares of its sides is 1250 sq. cm. Find the length of all the sides. a)a =16; b = 20; c =24 b)a =13; b = 20; c =27 c)a =15; b = 20; c =25 d)a =14; b = 21; c =25

26. Copyright © Ed2Net Learning, Inc. 26 10) The hypotenuse of a right triangle is 4 feet more than its longer leg. The length of shorter leg is 12 feet. Find the length of the longer leg and hypotenuse. a)16 ft; 20 ft b)18 ft; 22 ft c)8 ft; 12ft d)9 ft; 13 ft

27. Copyright © Ed2Net Learning, Inc. 27 You did a great job today!