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In the figure, AB = AD, ∠1 = ​∠2 and ​∠3 = ​∠4. Prove that AP = AQ.

cant because i dont know
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↵first make triangle APC​ CONGRUENCE TO ACQ
  • ​ANGLE 3=4
  • PC=CQ(C.P.C.T)
  • AC=AC
​​BY SAS
THEN IT CAN BE EASILY PROVED AP=AQ
​
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prove it by sas congruence rule
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angle1=angle2
angle3=angle4
1+3=2+4
angleBAC=angleDAC
In triangle BAC and triangle DAC
AB=AD(given)
angleBAC=angleDAC(proved)
AC=AC(commom side)
triangleBAC is congruent to triangleDAC by SAS congruence rule
angleACP=angleACQ(CPCT)
​In triangleACP and triangleACQ
​angle3=angle4(given)
​angleACP=angleACQ(proved)
​AC=AC(common side)
triangleACP is congruent to triangleACQ by ASA congruence rule
AP=AQ(CPCT)
​
 
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