Lost Our Noodles! Triangle Exploration
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- Arabella Agnes Hubbard
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1 Any three lengths will form a triangle. Lost Our Noodles! Triangle Exploration 1. Is this statement (Circle your answer.) 2. With your partner, measure each of the triangles (round to the nearest tenth) and record the answers in the table. Shape #1 Shape #2 Shape #3 Shape #4 3. Post your group s results on the class chart and then record the class results below. Record lengths in ascending order (the smallest length is Length 1). Shape Number Shortest Middle Longest Did the lengths form a triangle? 4. Can any three lengths form a triangle? Why or why not?
2 In every triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Would the lengths of 6 cm, 8 cm, and 10 cm form a triangle? Let s use the statement above to find out. Pair of s 6 cm and 8 cm 10 cm 8 cm and 10 cm 6 cm 6 cm and 10 cm 8 cm > > > 6 18 > > 8 16 > 8 Since the sums of the lengths of any two sides are greater than the third side, the lengths of 6 cm, 8 cm, and 10 cm would form a triangle. 5. Would the lengths of 3 cm, 5 cm, and 8 cm form a triangle? Why or why not? Pair of s, because 6. Would the lengths of 2 cm, 4 cm, and 7 cm make a triangle? Why or why not? Pair of s, because
3 Knowing that the sum of any two sides of a triangle must be greater than the length of the third side also helps us determine if a given value can be the length of an unknown side. Triangle ABC is shown at right. Which of the following could be the length of the third side of Triangle ABC? A 95 o A 19 feet B 20 feet C 19.5 feet D 14 feet Answer: A Is > 19? No, 19 = 19 so A is not correct. B Is > 20? No, 19 < 20 so B is not correct. C Is > 19.5? No, 19 < 19.5 so C is not correct. D Is > 14? Yes, 19 > 14 so D is the answer! C 8 feet 11 feet 51 o x 34 o B The angle measures also give us information about the length of the sides of Triangle ABC. Let s agree that the third side of Triangle ABC is 14 feet in length. 7. Arrange the lengths of the sides in order from least to greatest. 8. Arrange the angle measures in order from least to greatest. We can also write inequality statements to show these relationships. AC AB CB m B m C m A 9. What do you notice about the relationship between the order of the side lengths and the order of the angle measures? OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO Tell whether a triangle can have sides with the given lengths. Justify your answer cm, 6 cm, 13 cm in., 12 in., 3 in feet, 15 feet, 9 feet m, 10 m, 18 m
4 Use your noodle to answer the following questions. 14. Two of the sides of a triangular tile measure 3 inches and 4 inches. The length of the third side, in inches, is a whole number. a. Could the third side measure 1 inch? Why or why not? b. Make a list of the possible lengths for the third side. 15. In shop class, Connor wants to weld three lengths of pipe to make a triangle. The lengths of pipe are 3.5 feet, 8 feet and feet. Which of the following statements is true about the triangle Connor wants to build? A The triangle cannot be welded because < B The triangle can be welded because > 3.5. C The triangle can be welded because > 8. D The triangle can be welded because any two lengths of pipe are greater than the third length. 16. Could the three sides of a triangular piece of land measure 1 2 mile, 1 3 mile, and 3 mile? Why or why 4 not? (Use the table below to organize your work.) Pair of s 17. Triangle DEF is shown below. D Which of the following statements is NOT true about Triangle DEF? 53 o A DE EF B EF is the shortest side of Triangle DEF. C DF is the longest side of Triangle DEF. D EF DF E 90 o 37 o F
5 18. The map below shows the distance in air miles from Houston to both Austin and San Antonio. Austin miles Houston San Antonio miles What is the greatest possible distance from Austin to San Antonio? How do you know? 19. Two adjacent sides of an isosceles triangle measure 3 inches and 13 inches. Find the length of the third side. Explain how you determined this length. 20. A scale drawing of a triangular-shaped dog park shows that the sides measure 120 feet, 130 feet and 180 feet. Can these dimensions be correct? Why or why not? 21. Which of the following is a possible value for n if the sides of a triangle measure 4n, 2n and 5n? A 4 B 6 C 2 D all of the above 22. Triangle RST has side lengths of 17, Triangle WXY has angles that measure 60 o, and 24. Match each side with its correct 80 o and 40 o. Match each angle with its length. correct measure. R X 105 o 13 m 20 m 43 o 32 o S T W 17.6 m Y
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