5.5 Use Inequalities in a ∆ Mrs. vazquez Geometry.

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Presentation transcript:

5.5 Use Inequalities in a ∆ Mrs. vazquez Geometry

g-Co.2.7, 3.10 Essential Question: How do ∆ side measures relate with its opposite ∡? Objective: Students will find possible lengths of a ∆.

theorem 5.10 If one side of a ∆ is longer than another side, then the ∡ opposite the longer side is larger than the ∡ opposite the shorter side. A C B BC > AB, so m∡A > m∡C

theorem 5.11 If one ∡ of a ∆ is larger than another ∡, then the side opposite the larger ∡ is longer than the side opposite the smaller ∡. A C B m∡A > m∡C, so BC > AB

∆ Inequality theorem The sum of the lengths of any two sides of a ∆ is greater than the length of the third side. A B C AC + BC > AB

Find possible values for x A ∆ has one side of 11in and another of 15in. Describe the possible lengths of the third side. * find the value of x if x is the smallest side * find the value of x if x is the largest side * set solution as a compound inequality

Find possible values for x A ∆ has one side of 12in and another of 8in. Describe the possible lengths of the third side.