Question

In ∆ABC, ∠B = 90° and BD is perpendicular to hypotenuse AC then prove that ∆ADB ~ ∆BDC

Answer 1

Given : In ∆ABC ∠B = 90° and BD ⊥ AC

To prove : ∆ADB ~ ∆BDC

In ∆ABC

∠A + ∠C = 90° [∵ ∠B = 90°] …..(i)

In ∆BDC

∠DBC + ∠C = 90° [∵ ∠BDC = 90°] ……(ii)

From equation (i) and (ii)

∠A + ∠C = ∠DBC + ∠C

⇒ ∠A = ∠DBC …(iii)

Now, In ∆ADB and ∆BDC

∠ADB = ∠BDC = 90° (given)

∠DAB = ∠DBC (by eqⁿ(iii))

By A-A Similarly criterion

∆ADB ~ ∆BDC