Question

In the given diagram, ΔABC ∼ ΔPQR. If AD and PS are bisectors of ∠BAC and ∠QPR respectively then ______.

 

Options

• ΔABC ∼ ΔPQS

• ΔABD ∼ ΔPQS

• ΔABD ∼ ΔPSR

• ΔABC ∼ ΔPSR

Answer 1

In the given diagram, ΔABC ∼ ΔPQR. If AD and PS are bisectors of ∠BAC and ∠QPR respectively then ΔABD ∼ ΔPQS.

Explanation:

Here, ΔABC ∼ ΔPQR

∴ ∠A = ∠P

Then, `1/2 ∠A = 1/2 ∠P` or ∠BAD = ∠QPS  ...(i)

And ∠B = ∠Q   ...(ii)

In ΔABD and ΔPQS,

∠BAD = ∠QPS  ...[From (i)]

∠B = ∠Q   ...[From (ii)]

Then, ΔABD ∼ ΔPQS   ...(By AA similarity criterion)