Question

# In which of the following figure, the triangle formed by the line segment DE using the sides of the triangle ABC is similar to the triangle ABC?

Solution

## The correct option is C According to basic proportionality theorem, if DE || AB, then: ADCD=BECE ADCD+1=BECE+1 AD+CDCD=BE+CECE ACCD=BCCE ∠C is common ∠CDE=∠CAB as they are corresponding angles. ∠DEC=∠ABC as they are corresponding angles. So, △ABC∼△DEC. In the given options, DE||AB in only one the option shown above. This theorem will hence, hold only for this option.

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