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Download Geometry 5-5 Triangle Inequalities
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Transcript
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. C Smallest 12 5 A 9 B BC ∠A Biggest AB ∠C AC ∠B Examples • List the sides from shortest to longest. C 63° A 55° 62° B • List the angles from largest to smallest. 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. 4 +4 > 7 Can make a Δ 3 4 7 4 +3 > 7 Cannot make a Δ 3 +3 > 7 Cannot make a Δ Example • Can the following sets of numbers be the sides of a triangle? 19, 10, 7 7, 9, 6.2 21, 8, 13 Example Find the range of values that could be the third side of a triangle. Given: 6 and 15 Given: 40 and 11
