Question

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

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

Answer 1

The correct option is D CD = BD


Given: ΔBAC ≅ ΔEBD
∴ AB = BE (CPCT)
$\Rightarrow AB=BE=\frac{1}{2}AE$
⇒ 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).