Let ABC and A 39 B 39 C 39 be two triangles in which AB gt A 39 B 39 BC gt B 39 C 39 and CA gt C 39 ...........

Quantitative Aptitude (CDS) Coordinate Geometry

Let ABC and A'B'C' be two triangles in which AB > A'B', BC > B'C' and CA > C'A'. Let D, E and F be the mid-points of the sides BC, CA and AB, respectively. Let D', E' and F' be themid-points of the sides B'C',C'A' and A'B', respectively. Consider the following statements

$I. AD > A' D', BE > B' E' and\: CF > C'F' are \: always\: true.$

Which one of the following is correct in respect of the above statements?

Both Statement I and Statement II are true and Statement II is the correct explanation of Statement I

Both Statement I and Statement II are true but Statement II is not the correct explanation of Statement I

Statement I is true but Statement II is false

Statement I is false but Statement II is true

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Explanation:

Given, in $\Delta$ ABC and $\Delta$ A'B'C' AB> A'B', BC > B'C' and CA > C' A' and Statement I, which is always true, is as follows
AD> A'D', BE > B'E' and CF > C'F' where, D, E and F are mid-points of sides BC, CA and AB, respectively and D¢, E¢ and F¢ are mid-points of sides B'C', C' A' and A'B', respectively. Verification
Let in $\Delta$ ABC, each side = 4 and in $\Delta$ A'B'C', each side = 2
$\therefore$ AD = $\sqrt{16-4}=\sqrt{12}=2\sqrt{3}$