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Ch 5.4: Side Lengths of a Triangle Theorem: The sum of the lengths of 2 sides of a triangle is greater than the length of the 3rd side ‐‐‐> we only need to add the 2 shorter sides to see whether their sum is greater than the 3rd ‐‐‐> Which of the following may be the lengths of the sides of a triangle? (1) 2,3,5 (2) 4,4,8 (3) 3,4,8 (4) 5,6,7 1 Two sides of a triangle have lengths 2 and 5. Find all possible lengths of the 3rd side. 2 5.5‐ An Inequality Involving an Exterior Angle of a Triangle EXTERIOR ANGLE OF A POLYGON ‐an exterior angle of a polygon is an angle that forms a linear pair with one of the interior angles of the polygon ‐an exterior angle of a triangle is formed outside the triangle by extending a side of the triangle ‐for each exterior angle‐‐‐>there are 1 adjacent interior angles and 2 nonadjacent interior angles ‐‐‐‐‐>Theorem: the measure of an exterior angle of a triangle is greater than the measure of either nonadjacent interior angle 3 Use triangle ABC, where D is a point on AB. a) Name the exterior angle of triangle DCB at vertex D. b) Name the 2 nonadjacent interior angles of triangle DCB for the exterior angle given as the answer to a c) Write the theorem that allows us to say: m ADC > m DCB d) Write the postulate that allows us to say: m ACB > m DCB 4 Given: In triangle ABC, D is a point on AC AD≅BD Prove: m ABC > m A 5 Given: Isosceles triangle PQR PS bisects vertex RPQ RSQ is extended through Q and T Prove: a) m PQT > m QPS b)m PQT > m RPS 6 Homework: 5.4 pg 188 #1‐23odd and 5.5 pg 193 #1‐13odd,16,18,19 7