The correct statement is:

B. Each side length of triangle PQR is 2 times the corresponding side length of triangle P′Q′R′.

Explanation:

1. The triangles are likely similar based on the phrasing and structure of the options. Similar triangles have proportional side lengths but identical angle measures.
2. The problem implies that the sides of triangle $PQR$ are larger in proportion to the sides of triangle $P′Q′R′$.
3. If the scale factor between the triangles is $2$, then each side of $PQR$ is $2 \times$ the corresponding side of $P′Q′R′$, which matches option B.
4. Angles in similar triangles are congruent, so the sum of the angle measures is the same for both triangles, making option D false.
5. Triangle congruence (option C) requires equal side lengths and angles, which isn't indicated here.

Would you like me to explain proportionality in triangles further? Here are some related questions you might explore:

1. How do you determine if two triangles are similar?
2. What is the relationship between side lengths and angle measures in similar triangles?
3. How can you calculate the scale factor between two similar triangles?
4. What are the properties of congruent triangles compared to similar triangles?
5. How do you use proportions to find missing side lengths in similar triangles?

Tip: In similar triangles, always compare corresponding sides and angles carefully to determine the scale factor.