Math With Mrs. Swing



Name:Investigation: Triangle Inequality Theorem1) Choose a set of measurements from your table that do not form a triangle. _____ cm, _____ cm, _____ cmWhat is keeping these sides from forming a triangle? Explain using complete thoughts.2) Choose the short side and medium side from a row that didn’t make a triangle. ____ cm, _____ cmUse your ruler as the third side – what is the longest possible length the 3rd side can be and have it still form a triangle? At what length does it "flatten out"?What is the shortest possible length of the third side? What happens to the triangle when it gets shorter than this length?3) Patrick measured three sides 3 cm, 4 cm, and 13 cm and found that they do not form a triangle. What is keeping these sides from forming a triangle?4) Yael has two sides 5 cm and 10 cm, what is the longest possible length the 3rd side can be and have it still form a triangle? What is the shortest possible length of the third side?The Triangle Inequality Theorem states that Practice:1) Is it possible to form a triangle with these side lengths? Explain.a) 2 cm, 5 cm, 2 cmb) 3 in, 2.9 in, 6 inc) 112 mm, 300 mm, 190 mm2) Two sides of a triangle are given. What are ALL the possible lengths of the third side? (Hint: what is the longest possible side length, what is the shortest possible side length?)a) 10 in, 15 inb) 10 mi, 8 mic) 12 yd, 5 yd3) Kaitlin notices that a map of a triangular hiking route said that the entire hike was exactly 6 miles long. If each of the three connecting trails is a whole number of miles long, how long is each trail? (Draw a picture to help you)4) Angela needs a ladder to repair a second-story window. The window is 12 feet off the ground. Because there are bushes near the house, she must place the bottom of the ladder 5 feet from the edge of the house. Use the triangle inequality to figure out how long the ladder could be. (Draw a picture to help you) ................
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