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Question
In the figure, RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ ΔSAT.
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Solution
∠1 = 2∠2 and ∠4 = 2∠3
1 = 22 and 4 = 23∠1 = ∠4 ...(vertically opposite angles)
⇒ 2∠2 = 2∠3 or ∠2 = ∠3 ........(i)
∠R = ∠S = ...(since RT = TS and angle opposite to equal sides are equal)
⇒ ∠TRB = ∠TSA = .........(ii)
In ΔRBT and ΔSAT.
RT = TS
∠TRB = ∠TSA
∠RTB = ∠STA = ...(common)
Therefore, ΔRBT ≅ ΔSAT. ...(ASA criteria)
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