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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, ABCDEC.

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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