question_answer

 

Directions: Each of these questions contains two statements:

Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below.

Assertion [A] If in a \[\Delta ABC\], a line \[DE||BC\], intersects AB at D and AC at E, then\[\frac{AB}{AD}=\frac{AC}{AE}\].

Reason [R] If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are divided in the same ratio.

A) A is true, R is true; R is a correct explanation for A.

B) A is true, R is true; R is not a correct explanation for A.

C) A is true; R is False.

D) A is false; R is true.

Correct Answer: A

Solution :

Statement II is true.

For Assertion,

Since, \[DE\,|\,\,|\,\,BC\]

\[\therefore\] By Thales Theorem

\[\frac{AD}{DB}=\frac{AE}{EC}\Rightarrow \frac{DB}{AD}=\frac{EC}{AE}\]

\[\Rightarrow 1+\frac{DB}{AD}=1+\frac{EC}{AE}\]

\[\Rightarrow \frac{AD+DB}{AD}=\frac{AE+EC}{AE}\]

\[\Rightarrow \frac{AB}{AD}=\frac{AC}{AE}\]

\[\therefore\] Both Statement I and II are true and Statement II is correct explanation of statement I.