ΔABC ≅ ΔDEF by the SAS congruence theorem, hence, using the CPCTC theorem, ∠A ≅ ∠D.
What is the Side-angle-side Congruence Theorem (SAS)?
The side-angle-side congruence theorem (SAS) states that two triangles are congruent if they have a pair of included congruent angles and two pairs of congruent sides that are corresponding to each other.
What is the CPCTC Theorem?
The CPCTC theorem states that if two triangles are congruent, then every of their corresponding parts are congruent to each other.
Triangles ABC and DEF have:
Two pairs of congruent sides - AC ≅ FD and BC ≅ EF
One pair of congruent included angles - ∠C ≅ ∠F
Therefore, ΔABC ≅ ΔDEF by the SAS congruence theorem.
Since ΔABC ≅ ΔDEF, all its corresponding parts will be congruent to each other based on the CPCTC theorem.
Therefore, ∠A ≅ ∠D by CPCTC.
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