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Q.

Tell whether the following statement is true or false:

In the given figure, AD is the median and DE || AB. Then BE is the median.

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a

True

b

False

answer is A.

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Detailed Solution

Given a figure in which AD is the median and DE || AB.
In triangle ABC,AD is the median and DE, drawn parallel to side BA, meets AC at point E. Show that BE is also a median.

In triangle ABC,AD is the median and DE, drawn parallel to side BA, meets AC at point E. Show that BE is also a median.

As, AD is the median, BD = DC.
Now, as by mid-point theorem, the straight line drawn through the midpoint of one side of a triangle parallel to another bisects the third side.
As, DE is the bisector on side AC so, AE = EC.
Hence, BE is median.
Given statement is true.
Therefore, option 1 is correct.

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