Question : In the figure, AB = AD = 7 cm, and AC = AE, and BC = 11 cm, then find the length of ED.
Option 1: 12
Option 2: 10
Option 3: 11
Option 4: 2
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Correct Answer: 11
Solution :
Given, AB = AD = 7 cm, and AC = AE, and BC = 11 cm
$\angle BAC = \angle DAE$ (vertically opposite angles)
In the given figure, $\frac{AB}{BC}=\frac{AD}{ED}$
So, $\triangle ABC \cong \triangle ADE$ [by Side-Angle-Side criteria]
⇒ $ED = BC = 11$ cm
Hence, the correct answer is 11.
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