In $\Delta ABC$ and $\Delta DEF$, $\angle A = 50^\circ, \angle B = 70^\circ, \angle D = 60^\circ, \angle F = 50^\circ$. Then:
(a) $\Delta ABC \sim \Delta FDE$
(b) $\Delta ABC \sim \Delta DFE$
(c) $\Delta ABC \sim \Delta FED$
(d) $\Delta ABC \sim \Delta DEF$
Step-by-Step Solution
Key Concept: $\angle C = 180^\circ - (50^\circ+70^\circ) = 60^\circ$. $\angle E = 180^\circ - (60^\circ+50^\circ) = 70^\circ$. Matching: $A(50^\circ) \leftrightarrow F(50^\circ), B(70^\circ) \leftrightarrow E(70^\circ), C(60^\circ) \leftrightarrow D(60^\circ) \Rightarrow \Delta ABC \sim \Delta FED$? Wait: $A \leftrightarrow F, B \leftrightarrow E, C \leftrightarrow D \Rightarrow \Delta ABC \sim \Delta FED$.
$\angle C = 60^\circ$ and $\angle E = 70^\circ$. Angles match $A \leftrightarrow F, B \leftrightarrow E, C \leftrightarrow D \Rightarrow \Delta ABC \sim \Delta FED$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Matching corresponding angles $A(50^\circ) \leftrightarrow F(50^\circ), B(70^\circ) \leftrightarrow E(70^\circ), C(60^\circ) \leftrightarrow D(60^\circ)$: 1.0 Mark
Correct Answer: $\Delta ABC \sim \Delta FDE$