PAB AND QAC ARE TWO EQUILATERAL TRIANGLES DRAWN ON SIDES AB AND AC OF TRIANGLE ABC PROVE THAT PC=QB - Maths - Triangles

Question

PAB AND QAC ARE TWO EQUILATERAL TRIANGLES DRAWN ON SIDES AB AND AC
OF TRIANGLE ABC PROVE THAT PC=QB

Manbar Singh · Accepted Answer

Join PC and BQ
Now, ∠PAB = ∠QAC  Angles of equlateral ∆⇒∠PAB + ∠BAC = ∠QAC + ∠BAC⇒∠CAP = ∠BAQ   
1In ∆ACP and ∆ABQ,  AP = AB   As APB is an equilateral ∆CAP = ∠BAQ  using 1AC = AQ  As ACQ is an equilateral ∆∆ACP≅∆ABQ    SAS PC = BQ  CPCT

PAB AND QAC ARE TWO EQUILATERAL TRIANGLES DRAWN ON SIDES AB AND AC OF TRIANGLE ABC.PROVE THAT PC=QB