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] ABCD is a trapezium with \[DC||AB\]. E and F are points on AD and

BC respectively such that\[EF||AB\].

Then, \[\frac{AE}{ED}=\frac{BF}{FC}\].

Reason [R] Any line parallel to parallel sides of a trapezium divides the non-parallel sides proportionally.

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: B

Solution :

Given,  \[EF\,||AB\]

\[\therefore \,\,\,\,OE\,||\,AB\,\,|\,\,|\,CD\,\]          \[\left[ \because \,\,\,AB\,|\,|\,\,CD \right]\]

In \[\Delta ACD,\,\frac{AE}{ED}=\frac{AO}{OC}\]          \[\left[ by\,\,BPT \right]\]  … (i)

Similarly in  \[\Delta ABC,\,\frac{AO}{OC}=\frac{BE}{FC}\]                    ... (ii)

From Eqs. (i) and (ii),  \[\frac{AE}{ED}=\frac{BF}{FC}\]

\[\therefore\] Any line parallel to parallel sides of a trapezium divides the non-parallel sides proportionally.

Both Statement I and II are True and Statement II is the correct explanation of Statement I.