Question

given the figures with congruent angles and sides marked in each sketch, first list the parts of the figures that are corresponding and congruent (for example, in problem 1, ∠c ≅ ∠r). then determine if a reflection occurred as part of the sequence of transformations that was used to create the image.
1.
congruencies
∠c ≅ ∠r
reflected? yes or no

Explanation:

Step1: Identify corresponding sides and angles

From the markings, we have $\angle C\cong\angle R$. Also, the marked - side next to $\angle C$ in $\triangle ABC$ is congruent to the marked - side next to $\angle R$ in $\triangle RST$, and the other marked sides are congruent. Let's list all congruences: $\angle C\cong\angle R$, the side between $\angle C$ and the un - marked angle in $\triangle ABC$ is congruent to the side between $\angle R$ and the un - marked angle in $\triangle RST$, and the other marked sides are congruent.

Step2: Check for reflection

If we compare the orientation of the two triangles, we can see that the order of the vertices is reversed. In $\triangle ABC$ and $\triangle RST$, if we consider the order of vertices around the triangles, one is the mirror - image of the other. So, a reflection has occurred.

Answer:

Congruences: $\angle C\cong\angle R$, the side adjacent to $\angle C$ in $\triangle ABC$ is congruent to the side adjacent to $\angle R$ in $\triangle RST$, the other marked sides are congruent. Reflected? Yes