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Question
In the following Figure, DE || BC such that AE = (1/4) AC. If AB = 6 cm, find AD.
Solution
We have, DE || BC, AB = 6 cm and AE `= 1/4` AC
In ΔADE and ΔABC
∠A = ∠A [Common]
∠ADE = ∠ABC [Corresponding angles]
Then, ΔADE ~ ΔABC [By AA similarity]
`rArr"AD"/"AB"="AE"/"AC"` [Corresponding parts of similar Δ are proportional]
`rArr"AD"/6=(1/4AC)/"AC"` [∵ AE `=1/4` AC given]
`"AD"/6=1/4`
`rArr"AD"=6/4=1.5` cm
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