The problem is asking you to find missing measures, given that $\triangle ABC \cong \triangle DEF$. This means the two triangles are congruent, so their corresponding sides and angles are equal. Let’s solve the parts step-by-step:

Correspondences

• $\angle A \leftrightarrow \angle D$
• $\angle B \leftrightarrow \angle E$
• $\angle C \leftrightarrow \angle F$
• $AB \leftrightarrow DE$, $BC \leftrightarrow EF$, $AC \leftrightarrow DF$

Solutions

a) $m\angle A = m\angle D$

From the figure, $m\angle D = 65^\circ$.
So, $m\angle A = 65^\circ$.

b) $m\angle C = m\angle F$

From the figure, $m\angle F = 50^\circ$.
So, $m\angle C = 50^\circ$.

c) $EF = BC$

From the figure, $BC = 19$.
So, $EF = 19$.

d) $m\angle E = m\angle B$

The sum of angles in a triangle is $180^\circ$.
In $\triangle DEF$: $m\angle D + m\angle E + m\angle F = 180^\circ$ $65^\circ + m\angle E + 50^\circ = 180^\circ$ $m\angle E = 65^\circ$ Thus, $m\angle B = 65^\circ$.

e) $AC = DF$

From the figure, $AC = 15$.
So, $DF = 15$.

f) $DE = AB$

From the figure, $AB = 12$.
So, $DE = 12$.

Final Answers:

a) (m\angle A