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HW: pgs. 336-337 (4-9, 12-14, 34, 35) & pg. 343 (1-6, 9-14) www.westex.org HS, Teacher Website 12-11-14 Warm up—Geometry H B In the figure to the right, AB = BC and DE = EF = DF. If the measure of ABC is 30° E and the measure of BDE is 50°, D what is the measure of DFA? A F C Note: Figure not drawn to scale GOAL: I will be able to: 1. apply inequalities in one triangle. HW: pgs. 336-337 (4-9, 12-14, 34, 35) & pg. 343 (1-6, 9-14) www.westex.org HS, Teacher Website Name _________________________ Date ________ Geometry H 5.5 & 5.6 Inequalities in One & Two Triangle GOAL: I will be able to: 1. apply inequalities in one triangle. The positions of the ______________ and _______________ sides of a triangle are related to the positions of the largest and smallest angles. Example 1: Ordering Triangle Side Lengths and Angle Measures a. Write the angles in order b. Write the sides in order from from smallest to largest. shortest to longest. YOU TRY: a. Write the angles in order From smallest to largest. b. Write the sides in order from Shortest to longest. A triangle is formed by three segments, but not __________ set of three segments can form a triangle. A certain relationship must exist among the lengths of three segments in order for them to form a triangle. http://www.mathopenref.com/triangleinequality.html Example 2: Applying the Triangle Inequality Theorem Tell whether a triangle can have sides with the given lengths. Explain. a. 7, 10, 19 b. 2.3, 3.1, 4.6 c. n + 6, n2 – 1, 3n, when n = 4. YOU TRY: a. 8, 13, 21 b. 6.2, 7, 9 c. t – 2, 4t, t2 + 1, when t = 4 Example 3: Finding Side Lengths The lengths of two sides of a triangle are 8 inches and 13 inches. Find the range of possible lengths for the third side. YOU TRY: The lengths of two sides of a triangle are 22 inches and 17 inches. Find the range of possible lengths for the third side. Example 1: Using the Hinge Theorem and Its Converse a. Compare mBAC and mDAC. b. Compare EF and FG. c. Find the range of values for k. YOU TRY: a. Compare mEGH and mEGF. b. Compare BC and AB. 5.5 Practice 1. Write the angles in order from smallest to largest. 2. Write the sides in order from shortest to longest. 3. The lengths of two sides of a triangle are 17 cm and 12 cm. Find the range of possible lengths for the third side. 4. Tell whether a triangle can have sides with lengths 2.7, 3.5, and 9.8. Explain. 5. Ray wants to place a chair so it is 10 ft from his television set. Can the other two distances shown be 8 ft and 6 ft? Explain. 5.6 Practice 1. Compare mABC and mDEF. 3. Find the range of values for z. 2. Compare PS and QR.