Practice Set 1.2 | Q 4 | Page 14
Measures of some angles in the figure are given. Prove that `”AP”/”PB” = “AQ”/”QC”`
Given: ∠APQ = 60∘, ∠ABC = 60∘
To Proved: `"AP"/"PB" = "AQ"/"QC"`.
To Proved: `"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.
Solution:-
Given: ∠APQ = 60°, ∠ABC = 60°
To prove: AP/PB = AQ/QC
Proof: ∠APQ = ∠ABC = 60° (Given) Therefore, ∠APQ ≅ ∠ABC (By definition of congruent angles) PQ || BC (Corresponding angles test for parallel lines)
In ∆ABC, By Basic Proportionality Theorem, AP/PB = AQ/QC
Hence, Proved.
Chapter 1. Similarity- Practice Set 1.2 – Page 13
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