# 5.5 Inequalities in Triangles DOM Can you figure out the puzzle below??? Domino.

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5.5 Inequalities in TrianglesDomino

Comparison Property of InequalityComparison Property of Inequality:If a = b + c, and c > 0, then a > b.

Proof of Comparison Property of InequalityStatementsReasonsGiven: a = b + c, c > 0Prove: a > bc > 0b + c > b + 0b + c > ba = b + ca > b

TheoremInsert figure from home

ApplicationGiven the figure below, explain why .StatementsReasons1.

2.

3.1.

2.

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TheoremTheorem 5-10: If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side.Insert figure from home

ExampleList the angles of the following figure in order from smallest to largest.

TheoremTheorem 5-11: If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle.Insert figure from home

Sides of a TriangleList the sides of the following triangle in order from shortest to longest.Determine which segment is shortest in the following diagram.

TheoremTheorem 5-12: Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.Insert figure from home

TheoremCan a triangle have sides with the given lengths?a) 7 ft, 3 ft, 8 ftb) 10 cm, 6 cm, 3 cmA triangle has sides of lengths 8 cm and 10 cm. Describe the lengths possible for the third side.

5.5 Inequalities in TrianglesHW 5.5: #1-25 (1st column), 32, 33, 35p.192: #3-4, 11, 22, 24-26Scrambled Eggs

Midterm ReviewGiven the figure below, name the type of angle pairs given.

Midterm Review

Midterm ReviewFind x in the following polygon.x

Midterm ReviewFind the equation of a line parallel to y + 3x = 5 that goes through the point (-3, 5).Find the equation of a line that goes through the point (-2, 1) and (3,2).

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