Q. 205.0( 2 Votes )

# In ΔABC, ∠B = 90° and BD ⊥ AC. Prove that ∠ABD = ∠ACB.

Answer :

Let ∠ABD = x and ∠ACB = y

According to question,

∠B = 90^{O}

In triangle BDC, we have,

∠BDC = 90^{O}

∠DBC = (90 – x)^{O}

∠BDC + ∠DBC + ∠DCB = 180^{O}

90^{O} + (90 – x)^{O} + y = 180^{O}

180^{O} – x + y = 180^{O}

x = y

So,

∠ABD = ∠ACB

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