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Question
In the given diagram, ΔABC and ΔDEF (not drawn to scale) are such that ∠C = ∠F and `(AB)/(DE) = (BC)/(EF)`, then
Options
ΔABC ∼ ΔDEF
ΔBCA ∼ ΔDEF
ΔCAB ∼ ΔDEF
the similarity of given triangles cannot be determined.
MCQ
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Solution
The similarity of given triangles cannot be determined.
Explanation:
To prove two triangles are similar by SAS, the equal angle must be the included angle between the two proportional sides.
Here, you are given ∠C = ∠F, but the proportional sides given are `(AB)/(DE) = (BC)/(EF)` these sides meet at ∠B and ∠E, not at ∠C and ∠F.
So, SAS does not apply and with only one angle equality plus a ratio of non-including sides, similarity is not guaranteed.
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