Q) In the given figure, ∠ ADC = ∠ BCA, prove that Δ ACB ~ Δ ADC. Hence find if AC = 8 cm and AD = 3 cm.
Ans: In Δ ACB and Δ ADC,
∠ ADC = ∠ BCA (given)
∠ A = ∠ A (common angle)
Δ ACB ~ Δ ADC (by AA similarity identity)
Next, from above similar triangles, we get
BD = AB – AD = – 3 =
Therefore, BD = 55/3 cm.