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Published byMaurice Barber Modified over 8 years ago
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Students will be able to use inequalities involving angles and sides of triangles
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The angles and sides of triangles have special relationships involving inequalities
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Properties of Inequalities Addition Property If a > b and c ≥ d, then a + c > b + d Multiplication Property If a > b and c > 0, then ac > bc If a > b and c < 0 then ac < bc Transitive Property If a > b and b > c, then a > c
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UUse addition, subtraction, multiplication, and division properties to solve inequalities SSame idea as solving equations IIf you divide by a negative number remember to reverse to inequality symbol
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7x – 13 ≤ -20 8y + 2 ≥ 14 -3(4x – 1) ≥ 15 3x – 5x + 2 < 12
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If a = b + c and c > 0, then a > b Used to prove the corollary to the Triangle Exterior Angle Theorem What is the Triangle Exterior Angle Theorem?
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The measure of an exterior angle is greater than the measure of each remote interior angles of a triangle
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Why is m m<3? Why is m m<C?
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If two sides of a triangle are not congruent, the the larger angle lies opposite the longer side
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A town park is triangular. A landscape architect wants to place a bench at the corner with the largest angle. Which two streets form the corner with the larges angle?
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Now suppose the architect wants to place a drinking fountain at the corner with the second largest angle. Which two streets form the corner with the second largest angle?
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If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle
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<S = 24 and <O = 130. Which side of Δ SOX is the shortest side? Explain.
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In order to form or construct a triangle the sum of the two shortest sides must be greater than the largest side.
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Can a triangle have sides with the given lengths? 3 ft, 7 ft, 8 ft? 2 m, 6m, 9m? 4 yd, 6yd, 9yd?
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Use x to represent the third side You will need to write three inequalities. One to represent each side of the triangle it could be Then write an inequality that represents the answers
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A triangle has sides lengths of 4in and 7in. What is the range of possible side lengths for the third side?
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Pg. 328 # 6 – 29 all 24 problems
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