Geometry 5-5 Inequalities in Triangles Within a triangle: – the biggest side is opposite the biggest angle. – the smallest side is opposite the smallest.

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Triangle Inequalities

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Geometry 5-5 Inequalities in Triangles Within a triangle: – the biggest side is opposite the biggest angle. – the smallest side is opposite the smallest angle. A B C SmallestBiggest BC AB AC ∠ A ∠ C ∠ B

Examples List the sides from shortest to longest. List the angles from largest to smallest. A B C 55° 62° 63° DF = 23 DE = 14 EF = 12

Constructing Triangles The two shortest sides of a triangle must add up to be greater than the third side > 7 Can make a Δ 3 +3 > 7 Cannot make a Δ 4 +3 > 7 Cannot make a Δ

Example Can the following sets of numbers be the sides of a triangle? 19, 10, 7 21, 8, 13 7, 9, 6.2

Example Find the range of values that could be the third side of a triangle. Given: 6 and 15Given: 40 and 11