A straight line parallel to the side AC of triangle ABC intersects the sides AB and BC at points M and N
| December 26, 2020 | education
A straight line parallel to the side AC of triangle ABC intersects the sides AB and BC at points M and N, respectively. Find BN if MN = 13, AC = 65, NC = 28.
consider triangles ABC and MBN. they are similar (the total angle and the corresponding angles for parallel lines are equal) => MN: AC = BN: BC = kk = 13/65 = 1/5 BC = BN + NC, then: BN / (BN + 28) = 1 / 5 by proportion method: BN + 28 = 5BN; 4BN = 28; BN = 7
Answer: BN = 7
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