The proof is; △BAD is congruent to △CDA using only congruence and no CPCTC.
To prove BAD≅△CDA using congruence.
Given: BD ⊥ AC, BA ⊥ DC
∠ABC and ∠ADC are right angles (definition of perpendicular lines)
∠BAC and ∠CAD are complementary angles
∠BAC and ∠CAD are both right angles (definition of complementary angles)
△BAD and △CDA both have a right angle and ∠BAC ≅ ∠CAD
By Angle-Angle (AA) congruence, △BAD≅△CDA
This proves △BAD is congruent to △CDA using only congruence and no CPCTC.