QQuestion
In the given diagram, △ABC ∼ △PQR. If AD and PS are bisectors of ∠BAC and ∠QPR respectively, then:
(a) △ABC ∼ △PQS
(b) △ABD ∼ △PQS
(c) △ABD ∼ △PSR
(d) △ABC ∼ △PSR
✓Answer
(b) △ABD ∼ △PQS
Explanation:
Given, △ABC ∼ △PQR.
Therefore, ∠A = ∠P and ∠B = ∠Q.
Since AD and PS bisect ∠A and ∠P respectively:
∠BAD = \frac{1}{2}∠A
and ∠QPS = \frac{1}{2}∠P
Since ∠A = ∠P:
∠BAD = ∠QPS
Also, ∠ABD = ∠PQS because ∠B = ∠Q.
Hence, △ABD ∼ △PQS by the AA criterion.
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