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TRIANGLE INEQUALITIES CHAPTER 5 (5.3, 5.5, 5.6) 5.3– Inequalities of One Triangle 1. Measure and label the sides and angle measures of each triangle below: L 2. Put the angles in order from least to greatest using inequalities. 3. Put the sides in order from shortest to longest using inequalities. A K C B Angles: ____________________ Sides: _____________________ M Angles: ____________________ Sides: _____________________ T W Y R V Angles: ____________________ Sides: _____________________ Angles: ____________________ Sides: _____________________ How are inequalities related to sides and angles of triangles? X EX: List the sides in order from longest to shortest. EX: List the angles in order from smallest to largest. Exterior Angle Inequality Theorem 3 1 2 4 Kuta Software - Infinite Geometry Name___________________________________ Inequalities in One Triangle Date________________ Period____ Order the angles in each triangle from smallest to largest. 1) 2) 16 yd L K J 18 cm 14 yd 18 yd L 13 cm M 20 cm K 3) In ∆RQP QP = 15 ft RP = 25 ft RQ = 13 ft 4) In ∆TUV UV = 17 yd TV = 14 yd TU = 9 yd Name the largest and smallest angle in each triangle. 5) 6) D 20 ft 16 ft C Y 17 ft 19 ft B 7) In ∆UVW VW = 13 m UW = 11.7 m UV = 5.8 m ©M X2O0Z1B17 3K5umtbaW ASfoRfstTwNaEroeG zLYL1Ck.u b mAMlVlw crcisgKh7tqsW VrZehsNefr5vOeJd1.9 3 4MBapdter MwxiWtXhA 8IFn4fDiineiOtpe2 fGxeJo1mSeStjroy0.i X 17 ft 20 ft W 8) In ∆EFG FG = 10.9 in EG = 17 in EF = 10.9 in -1- Worksheet by Kuta Software LLC Order the sides of each triangle from shortest to longest. 9) 10) F L 98° 46° M 55° 36° 63° 62° N E G 11) In ∆VWX m∠V = 50° m∠W = 48° m∠X = 82° 12) In ∆STU m∠S = 50° m∠T = 70° m∠U = 60° Name the longest and shortest side in each triangle. 13) A 14) F 66° 46°102° C 48° B 15) In ∆DEF m∠D = 35° m∠F = 95° E 66° D 16) In ∆KLM m∠K = 50° m∠L = 100° m∠M = 30° Critical thinking questions: 17) In triangle ABC: AB is the longest side. 70° is the measure of angle B. 18) In triangle XYZ: XY is the shortest side. 30° is the measure of angle Y. Find the range of possible measures for angle A. ©j q2w0q1N1k iKpuHtaa2 ISHohfYtlwMaGrxe9 GLzLzCA.5 6 7AXlXlj YrditgJhvtosI brce0sHeZrmvye8d3.6 8 lMda6deeT gwli0tsh2 NIQnlfRiLn0i6tneI tG3e6osmteJtwrbyh.F Find the range of possible measures for angle X. -2- Worksheet by Kuta Software LLC 5.5– Triangle Inequality Theorem 1. Draw a triangle with side lengths of 3cm, 4cm, 5cm. 2. Draw a triangle with side lengths of 3cm, 5cm, 7cm. 3. Draw a triangle with side lengths of 3cm, 3cm, 6cm. 4. Draw a triangle with side lengths of 4cm, 5cm, 11cm. Triangle Inequality Theorem Examples: Could the following side lengths make a triangle? Why or why not? 1) 5, 7, 9 2) 3, 2, 11 3) 6, 7, 13 4) 21, 18, 12 5) 7, 14, 7 6) 5, 21, 24 Examples: What are the possible values for the third side of the triangle? 1) x, 7, 4 2) 13, x, 8 3) 4, 4, x 4) 6, 11, x‐2 5) x+1, 14, 9 5.6– Inequalities in Two Triangles Find the measurements of the lengths of the segments and the measures of the angles between them. Hinge Theorem Converse of the Hinge Theorem EX: Which angle (∠1 or ∠2) is smaller? EX: Given that ST PR , PT = 12 and SR = 10, how does ∠PST compare to ∠SPR? EX: Find the value of x. EX: Name the longest segment in figure ABCD. Section 5-6 Worksheet Inequalities in Two Triangles I. Complete with <, >, or =. 1. AB _______ DE 4. m1 _______ m2 m1 _______ m2 2. FG _______ LM 3. 5. 6. m1 _______ m2 MS _______ LS II. Match the conclusion on the right with the given information. Use the diagram below. _______ 7. AB BC , 1 m2 A. m7 m8 _______ 8. AE EC , AD CD B. AD AB _______ 9. m9 m10, BE ED C. m3 m4 m5 m6 _______ 10. AB BC , AD CD D. AE EC III. Use the inequality to describe the restriction on the value of x as determined by the Hinge Theorem or its converse. 11. 12. 13.