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Question

In the figure given below, p, q, r are parallel lines; l and m are two transversals.

Consider the following:

1. AB : AC = DE : DF

2. AB × EF = BC × DE

Which of the above is/are correct?

This question was previously asked in
CDS I 2018 Elementary Mathematics Previous Year Paper (04-Feb-2018)
The correct answer is

Both 1 and 2

Construct a perpendicular from A to the line CF, Let it meet BE at O and CF at P

Similarly a perpendicular from D is drawn to the line CF, let it meet BE and CF at R and S

In triangle ABO and ACP

∠A is common and ∠O = ∠P = 90°

ABO ∼ ACP

∴ AB/AC = AO/AP

In triangle DRE and DSF

∠D is common and ∠R = ∠S = 90°

DRE ∼ DSF

∴ DE/DF = DR/DS

Parallel lines are equally spaced

∴ AO = DR and AP = DS

∴ AB/AC = DE/DF

So statement 1 is correct

AB/ (AC - AB) = DE/ (DF - DE)

AB/BC = DE/EF

∴ AB × EF = BC × DE

So statement 2 is also correct

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