Use the information given in the following figure to prove triangles ABD and CBD are congruent.

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asked Jun 12 in Class VII Maths by muskan15 (-3,437 points)

Use the information given in the following figure to prove triangles ABD and CBD are congruent.
Also, find the values of x and y.

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answered Jun 12 by aditya23 (-2,140 points)

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 △ABD and △CBD

BD = BD (common)

 AB = BC (given)

AD = CD (given)

∴ △ABD ≅ △CBD (SSS axiom)

 ∴ ∠ABD = ∠CBD

=> 50 = x + 5° => x = 50° - 5 = 45°

and ∠ADB  =  ∠CDB

⇒   y - 7° = 38° ⇒   y = 38° + 7° = 45°

Hence x = 45°, y = 45°

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