In the given figure, Δ ABC is isosceles and AP x BQ = AC², prove that Δ ACP ∼ Δ BCQ.
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Question

In the given figure, Δ ABC is isosceles and AP x BQ = AC2, prove that Δ ACP ∼ Δ BCQ.

KnowledgeBoat · Accepted Answer

Given, ⇒ AP x BQ = AC2 ⇒ AP x BQ = AC x AC ⇒ AP x BQ = AC x BC (From figure, AC = BC) ⇒ ........................(1) Since, AC = BC ⇒ ∠CAB = ∠CBA ...............(2) [Angles opposite to equal sides are equal] ⇒ 180° - ∠CAB = 180° - ∠CBA ⇒ ∠CAP = ∠CBQ ...................(3) In Δ ACP and Δ BCQ, ⇒ ∠CAP = ∠CBQ [From equation (3)] ⇒ [From equation (1)] ∴ Δ ACP ∼ Δ BCQ (By SAS postulates) Hence, proved that Δ ACP ∼ Δ BCQ.

Mathematics

In the given figure, Δ ABC is isosceles and AP x BQ = AC², prove that Δ ACP ∼ Δ BCQ.

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