The theorem that justifies why both triangles are congruent is: SAS congruence theorem.
What is the SAS Congruence Theorem?
The SAS congruence theorem states that two triangles having two pairs of congruent sides and a pair of included congruent angles are considered congruent triangles.
Thus:
ΔBAD and ΔCDA have the following:
- One pair of non-included right angles: ∠BAD ≅ ∠CDA
- Two pairs of congruent sides: BD ≅ AC and AD ≅ DA
Therefore, the theorem that justifies why both triangles are congruent is: SAS congruence theorem.
Learn more about the SAS congruence theorem on:
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