In the figure given below ΔABC is isosceles as AB = AC and CA are produced to Q and P such that AQ = AP

Question

In the figure given below ΔABC is isosceles as \(\overline{AB} = \overline{AC}; \overline{BA}\, and\, \overline{CA}\) are produced to Q and P such that \(\overline{AQ} = \overline{AP}\). Show that \(\overline{PB} = \overline{QC}\) 

(Hint: Compare ΔAPB and ΔACQ)

Answer 1

Given that ΔABC is isosceles and 

AP = AQ 

Now in ΔAPB and ΔAQC 

AP = AQ (given) 

AB = AC (given) 

∠PAB = ∠QAC (∵ Vertically opposite angles) 

∴ ΔAPB ≅ ΔAQC (SAS congruence)

∴ \(\overline{PB} = \overline{QC}\) (CPCT of ΔAPB and ΔAQC)