Question

use the two triangles below to answer the following questions.
enter a congruence statement about the two triangles.
to enter a congruence statement, type
cong(triangle(vertices), triangle(vertices)). for instance,
cong(triangle(pqr), triangle(xyz)) yields the statement $\triangle pqr \cong \triangle xyz$

Explanation:

Step1: Identify congruent parts

In $\triangle ABC$ and $\triangle DEF$ (wait, actually looking at the angles: $\angle A$ and $\angle D$ are right angles (marked), $BC$ and $EF$ are marked equal (the tick marks), and $\angle B$ and $\angle E$ seem corresponding. Wait, let's match vertices: $\angle A$ (right) in $\triangle ABC$, $\angle D$ (right) in $\triangle DEF$; side $BC = EF$ (tick marks); $\angle B$ and $\angle E$ are the other acute angles. So the congruence should be $\triangle ABC \cong \triangle DEF$? Wait no, let's check the labels. Wait the first triangle is $A$, $B$, $C$ with right angle at $A$, the second is $D$, $E$, $F$ with right angle at $D$, and $BC$ and $EF$ are equal (the middle sides with ticks). So by AAS or SAS? Wait, right angle, one side, and one angle. So the correct congruence statement is $\triangle ABC \cong \triangle DEF$? Wait no, let's see the vertices. Wait the first triangle: $A$ (right), $B$ (top), $C$ (bottom). Second: $D$ (right), $E$ (top), $F$ (bottom). So $\angle A \cong \angle D$ (right angles), $BC \cong EF$ (marked), $\angle B \cong \angle E$ (so AAS). So the congruence statement is $\triangle ABC \cong \triangle DEF$? Wait no, maybe $\triangle ABC \cong \triangle DEF$? Wait the example is cong(triangle(PQR), triangle(XYZ)) gives $\triangle PQR \cong \triangle XYZ$. So we need to write cong(triangle(ABC), triangle(DEF))? Wait no, let's check the angles. Wait $\angle A$ is right, $\angle D$ is right. $BC$ and $EF$ are equal. So the triangles are $\triangle ABC$ and $\triangle DEF$? Wait maybe $\triangle ABC \cong \triangle DEF$? Wait the correct congruence statement should match corresponding vertices. So $\angle A \cong \angle D$, $\angle B \cong \angle E$, $BC \cong EF$ (or $AC \cong DF$? Wait no, the middle sides (the ones with ticks) are $BC$ and $EF$. So $BC = EF$, $\angle A = \angle D = 90^\circ$, $\angle B = \angle E$. So by AAS, $\triangle ABC \cong \triangle DEF$. So the congruence statement is $\triangle ABC \cong \triangle DEF$, which in the required format is cong(triangle(ABC), triangle(DEF)).

Step2: Write the congruence statement

Using the format, we type cong(triangle(ABC), triangle(DEF)) which gives $\triangle ABC \cong \triangle DEF$.

Answer:

cong(triangle(ABC), triangle(DEF))