In Delta ABC and Delta DEF,angle A cong angle | vedclass

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(A) Given that $\angle A \cong \angle E$,so $m \angle A = m \angle E$.Given the equation $m \angle A + m \angle B = m \angle D + m \angle E$.Substitut

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(A) Given that $\angle A \cong \angle E$,so $m \angle A = m \angle E$.Given the equation $m \angle A + m \angle B = m \angle D + m \angle E$.Substituting $m \angle A = m \angle E$ into the equation,we get $m \angle E + m \angle B = m \angle D + m \angle E$.Subtracting $m \angle E$ from both sides,we get $m \angle B = m \angle D$.Since two angles of $\Delta ABC$ are congruent to two angles of $\Delta DEF$ (specifically $\angle A \cong \angle E$ and $\angle B \cong \angle D$),by the $AA$ similarity criterion,the triangles are similar.The correspondence must match the congruent angles: $A$ corresponds to $E$,$B$ corresponds to $D$,and therefore $C$ must correspond to $F$.Thus,the correspondence is $ABC \leftrightarrow EDF$.

In $\Delta ABC$ and $\Delta DEF$,$\angle A \cong \angle E$ and $m \angle A + m \angle B = m \angle D + m \angle E$. Then the correspondence $ABC \leftrightarrow \ldots$ between them is a similarity.

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