Question

In triangle ABC, mZA = 40° and m/B = 70°. Which statements about triangle ABC are true?

AB> AC
AB > BC
AB AC >BC
AC AC=AB
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Answer 1

AB > BC , AC > BC , AC = AB

Explanation:

the sum of the 3 angles in a triangle = 180° , that is

∠ A + ∠ B + ∠ C = 180°

40° + 70° + ∠ C = 180°

110° + ∠ C = 180° ( subtract 110° from both sides )

∠ C = 70°

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the longest side in a triangle is opposite the largest angle

the shortest side in a triangle is opposite the smallest angle

AB is opposite ∠ C and BC is opposite ∠ A

then AB > BC ( since ∠ C > ∠A )

similarly

AC > BC ( since ∠ B > ∠ C

note that ∠ B = ∠ C , thus the triangle is isosceles with the 2 legs congruent, so

AC = AB