Show NAME _____________________________________________ DATE ____________________________ PERIOD _____________Chapter 537Glencoe Geometry5-6 Study Guide and InterventionInequalities in Two TrianglesHinge TheoremThe following theorem and its converse involve the relationship between the sides of two triangles andan angle in each triangle.Hinge TheoremIf two sides of a triangle are congruent to two sides ofanother triangle and the included angle of the first is largerthan the included angle of the second, then the third sideof the first triangle is longer than the third side of thesecond triangle.RT>Converse of theHinge TheoremIf two sides of a triangle are congruent to two sides ofanother triangle, and the third side in the first is longerthan the third side in the second, then the included anglein the first triangle is greater than the included angle in thesecond triangle.m∠M > m∠Example 1:Compare the measures of??̅̅̅̅and??̅̅̅̅Two sides of△HGFare congruent to two sides of△HEF, andm∠GHF>m∠EHF. By the HingeTheorem,GF>ACR.FE. Which of the following inequalities theorem is applicable in two triangles?According to triangle inequality theorem, for any given triangle, the sum of two sides of a triangle is always greater than the third side.
Is it possible to form a triangle with the given side lengths 2ft 3ft 4ft?ANSWER: No; 11. SOLUTION: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
What is triangle inequality theorem?triangle inequality, in Euclidean geometry, theorem that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c. In essence, the theorem states that the shortest distance between two points is a straight line.
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5 6 study guide and intervention inequalities in two triangles
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