The Postulate that is used to prove triangle ABC ≅ triangle ADC is SAS Congruence Postulate .
In the question ,
it is given that ,
AD ≅ AB ,
AB is perpendicular to BC , that is AB ⊥ BC
and AD is perpendicular to DC , that is AD ⊥ DC .
Now , in triangle ABC and triangle ADC ,
Side AB = Side AD ......given
angle B = angle D = 90° .....because AB ⊥ BC and AD ⊥ DC .
Side AC = Side AC ......because common side
hence , triangle ABC ≅ triangle ADC by SAS Congruence Postulate .
Therefore , The Postulate that is used to prove triangle ABC ≅ triangle ADC is SAS Congruence Postulate .
Learn more about Congruence here
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