CBSE BoardEnglish MediumSTD 10MathsTriangles1 Mark
MCQ
In the given figure, if $\angle\text{ADE}=\angle\text{ABC},$ then CE =
A
$2$
B
$5$
✓
$\frac{9}{2}$
D
$3$
✓
Answer
Correct option: C.
$\frac{9}{2}$
Given: $\angle\text{ADE}=\angle\text{ABC}$ To find: The value of CE
Since $\angle\text{ADE}=\angle\text{ABC}$
$\therefore\text{DE}||\text{BC}$ (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 $\triangle\text{ABC},\ \text{DE}||\text{BC}$
$\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}$
$\frac{2}{3}=\frac{3}{\text{EC}}$
$\text{EC}=\frac{3\times3}{2 }$
$\text{EC}=\frac{9}{2}$
Hence we got the result C.
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