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. |
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