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प्रश्न
Use the information given in the following figure to prove triangles ABD and CBD are congruent. Also, find the values of x and y.
उत्तर
Given: In the figure AB = BC, AD = DC
∠ABD = 50, ∠ADB = y − 7°
∠CBD = x + 5°, ∠CDB = 38°
To find: The value of x and y
In Δ ABD and Δ CBD
BD = BD ........(common)
AB = BC ........(given)
AD = CD ...........(given)
∴ Δ ABD ≅ Δ CBD .........(SSS axiom)
∴ ∠ABD = ∠CBD
⇒ 50 = x + 50°
⇒ x = 50° − 5° = 45°
and ∠ADB = ∠CDB
⇒ y − 7° = 38°
⇒ y = 38° + 7° = 45°
Hence x = 45°, y = 45°
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