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Question

In the given figure, if ΔBAC ≅ ΔEBD, then which of the following is not always true?

A
AC || BD
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B
AE = 2AB
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C
BC || DE
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D
CD = BD
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Solution

The correct option is D CD = BD

Given: ΔBAC ≅ ΔEBD
∴ AB = BE (CPCT)
AB=BE=12AE
⇒ AE = 2AB
Also, ∠BAC = ∠EBD (CPCT)
⇒ AC || BD (∵ Corresponding angles are equal)
And, ∠ABC = ∠BED (CPCT)
⇒ BC || DE (∵ Corresponding angles are equal)
Thus, CD = BD is not always true.
Hence, the correct answer is option (d).

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