SOLUTION: ABC is a triangle. D is a point on AB such that AD = 1/4 AB and E is a point on AC such that AE= 1/4 AC. Prove that DE = 1/4 BC.

Question 1013432: ABC is a triangle. D is a point on AB such that AD = 1/4 AB and E is a point on AC such that AE= 1/4 AC. Prove that DE = 1/4 BC.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i believe you're going to find that triangle ABC is similar to triangle ADE by SAS.

SAS in this case means that corresponding sides are proportional and the angle between them are equal.

the sides that are proportional are AD to AB and AE to AC.

assuming AD = 1/4 and DB = 3/4, then ratio of AD to AB = 1/4 to 1.

assuming AE = 1/4 and EC = 3/4, then ratio of AE to AC = 1/4 to 1.

the angle between the corresponding sides is angle A.

the ratio of two corresponding sides of triangle ADE and triangle ABC are proportional and the corresponding angle between them is congruent (it's the same angle A), means the triangles are similar.

if the triangles are similar, then all the corresponding sides are proportional by the same common ratio which means that DE is proportional to BC by the same ratio which is (1/4) / 1.

this means that DE is 1/4 * the length of BC

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