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Question
Measures of some angles in the figure are given. Prove that `"AP"/"PB" = "AQ"/"QC"`.
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Solution
Given: ∠APQ = 60∘, ∠ABC = 60∘
To Prove: `"AP"/"PB" = "AQ"/"QC"`.
Proof:
∠APQ = ∠ABC = 60∘ ...(Given)
∴ ∠APQ ≅ ∠ABC
∴ Seg PQ || Seg BC ...(Corresponding angles test for parallel lines )(I)
In ΔABC,
Seg PQ || Seg BC ...[From I]
By Basic proportionality theorem,
∴ `"AP"/"PB" = "AQ"/"QC"`
Hence proved.
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