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

Question

Philoid · Accepted 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