Question
In the figure below, △ABC ≅ △BED, ∠DEB = 115∘ and ∠CAB = 25∘. It can be concluded that BC||ED.
Answer: Option A
:
A
Since ΔABC≅ΔBED,∠DBE=∠CAB=25∘(CPCT)And,∠DEB=∠CBA(CPCT)Now,∠BDE+∠DBE+∠BED=180∘⇒∠BDE+25∘+115∘=180∘⇒∠BDE=40∘Also,∠CBA+∠CBD+∠DBE=180∘(Linear set of angles)⇒∠CBA+25∘+115∘=180∘⇒∠CBA=40∘⇒∠BDE=∠CBDand they are alternate angles, soBC||ED.
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:
A
Since ΔABC≅ΔBED,∠DBE=∠CAB=25∘(CPCT)And,∠DEB=∠CBA(CPCT)Now,∠BDE+∠DBE+∠BED=180∘⇒∠BDE+25∘+115∘=180∘⇒∠BDE=40∘Also,∠CBA+∠CBD+∠DBE=180∘(Linear set of angles)⇒∠CBA+25∘+115∘=180∘⇒∠CBA=40∘⇒∠BDE=∠CBDand they are alternate angles, soBC||ED.
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