Question

In figure, AB= AD, angle 1 and 2 are equal and angle 3 and 4 are equal. Prove that AP = AQ..

Answer 1

to prove-AB=AQ
PROOF
AD=AB-GIVEN
A.3=A.4 AND A.1=A.2-GIVEN
SO,A.2+A.3=A.1+A.4
 ie,A.BAC=A.DAC
AC-COMMON
TRI.ABC IS SO CONGR.T TO TRI.ADC
HENCE BCA=DCA -CPCT
A.3=A.4 -GIVEN
AC IS COMMON
SO,TRI.APC IS CONGR.T TO TRI.AQC BY ASA
THEREFORE, AP=AQ -CPCT
HOPE THIS HELPS :-)...

Answer 2

To Prove: AB = AQ
PROOF:
AD=AB(Given)
Angle 3=Angle 4(Given)
 Angle 1=Angle 2(Given)
SO,Angle 2+Angle 3=Angle 1+Angle 4
i.e.,Angle BAC=Angle DAC
AC (Common)
Triangle ABC is cogruent to Triangle ADC
Hence, Angle BCA= Angle DCA (C.P.C.T.)
Angle 3=Angle 4 (Given)
AC (Common)
SO,Triangle APC is congruent to Tringle AQC (ASA rule)
So, AP=AQ (C.P.C.T.)