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Question

ABC is an acute angled triangle. DE is drawn parallel to BC as shown. Which of the following are always true?

i) ABC ADE

ii) ADBD=AEEC

iii) DE=BC2


  1. (i), (ii) and (iii)

  2. (ii) and (iii) only

  3. (i) and (ii) only

  4. Only (i)


Solution

The correct option is C

(i) and (ii) only


Consider ADE and ABC

Since DE || BC,
ADBD=AEEC
(by basic proportionality theorem)

BAC=DAE (common in both the triangles)

ADEABC (by SAS similarity criterion)

ADAB=DEBC=AEAC
(corresponding sides of similar triangles are in same ratio)

Now, DE=BC2 only if

ADAB=DEBC=AEAC=12

i.e. D and E should be the midpoints of AB and AC respectively.
So this may not be true always.

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