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Question
ABC is a triang 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.
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Solution
Let P and Q be the midpoints of AB and AC respectively.
Then PQ || BC such that
PQ = `1/2` BC ......(i)
In ΔAPQ, D and E are the midpoint of AP and AQ are respectively
∴ DE || PQ and DE = `1/2` PQ ....(ii)
From (1) and (2) DE = `1/2 PQ = 1/2 PQ = 1/2 (1/2 BC) `
DE = `1 /4`BC
Hence, proved.
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