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Warm-up: Solve for x and classify the triangle. (5x + 2) (6x + 5) (4x + 8) (9x + 7) (4x + 8) (9 – x)

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How long must each side of the drawbridge be so that the bridge spans the river when both sides come down?

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Can you form a triangle using any three lengths??

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Investigate: Instructions: Get a straw and a ruler Pick a number 1-8 Cut the straw the length of the number you chose. (in inches) Please throw the extra away so you don’t get confused. Now find 2 other people and try to make a triangle with your straw. Record the combinations. Some combinations will work, others won’t. You need to fill up the entire graph with no repetitions of the same combination. When you are finished please throw the straw away, put the ruler back, and have a seat. We will discuss when everyone finishes and try to fill in the Triangle Sum Conjecture.

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Triangle Inequality Conjecture The sum of the lengths of any two sides of a triangle is __________ the length of the third side. Ex 1: Which of the following segments could form a triangle? A. 6, 8, 10 B. 3, 3, 3 C. 2, 3, 5 D. 8, 2, 9 E. 10, 3, 4 F. 1, 1, 2

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EX 2: Find the range of possible side lengths for the third side of the triangle. 1.6 and 11 2.17 and 22 3.78 and 111

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Ex 3: Ordering Triangle Side Lengths and Angle Measures Write the angles in order from smallest to largest.

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Ex 4: Ordering Triangle Side Lengths and Angle Measures Write the sides in order from shortest to longest.

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EX 5: Solve for x. 120 x

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EX 6: Solve for x. 120 (x + 9) (2x – 3)

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EX 7:Find the missing angles. 46 65 1 2 5 4 3 82 142

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Triangle Inequality Theorem. The sum of the two shorter sides of any triangle must be greater than the third side. Example: 3 + 5 > 7 8 > 7 Yes!

Triangle Inequality Theorem. The sum of the two shorter sides of any triangle must be greater than the third side. Example: 3 + 5 > 7 8 > 7 Yes!

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