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Question
In the given figure, if ∠ADE = ∠ABC, then CE =
Options
2
5
9/2
3
Solution
Given: `∠ ADE = ∠ ABC`
To find: The value of CE
Since `∠ ADE = ∠ ABC`
∴ DE || BC (Two lines are parallel if the corresponding angles formed are equal)
According to basic proportionality theorem if a line is parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.
In ∆ABC, DE || BC
`(AD)/(DB)=(AE)/(EC)`
`2/3=3/EC`
`EC=(3xx3)/2`
`EC =9/2`
Hence we got the result `C`
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