 Students will be able to use inequalities involving angles and sides of triangles

 The angles and sides of triangles have special relationships involving inequalities

 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

UUse addition, subtraction, multiplication, and division properties to solve inequalities SSame idea as solving equations IIf you divide by a negative number remember to reverse to inequality symbol

 7x – 13 ≤ -20  8y + 2 ≥ 14  -3(4x – 1) ≥ 15  3x – 5x + 2 < 12

 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?

 The measure of an exterior angle is greater than the measure of each remote interior angles of a triangle

 Why is m m<3?  Why is m m<C?

 If two sides of a triangle are not congruent, the the larger angle lies opposite the longer side

 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?

 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?

 If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle

 <S = 24 and <O = 130. Which side of Δ SOX is the shortest side? Explain.

 In order to form or construct a triangle the sum of the two shortest sides must be greater than the largest side.

 Can a triangle have sides with the given lengths?  3 ft, 7 ft, 8 ft?  2 m, 6m, 9m?  4 yd, 6yd, 9yd?

 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

 A triangle has sides lengths of 4in and 7in. What is the range of possible side lengths for the third side?

 Pg. 328  # 6 – 29 all  24 problems