Question

Prove that Δ ABD ≈ Δ CBD. Find the values of x and y if angle ABD is 35 degree and angle CBD is (3x + 5)0angle ADB = (y -3)0and angle CDB = 250.

Answer 1

Given : Δ ABD and Δ CBD

∠ABD =  35° ,  ∠CBD =(3x + 5)°

∠ADB =  (y-3)°  ∠CDB = 25 °

To Find : Prove that Δ ABD ≈ Δ CBD.

Solution:

Δ ABD and Δ CBD

AB  = BC   ( given)

BD = BD   ( common)

AD = CD   ( given)

=> Δ ABD ≅ Δ CBD  (SSS)

Congruent Triangles: corresponding angles and sides are congruent

=> ∠ABD = ∠CBD

   ∠ADB = ∠CDB

∠ABD = ∠CBD

∠ABD =  35°

∠CBD =(3x + 5)°

Equating Both

=> 3x + 5 = 35

=> 3x = 30

=> x = 10

 ∠ADB = ∠CDB

∠ADB =  (y-3)°

∠CDB = 25 °

Equating Both

=> y  -3  = 35

=> y = 28

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