How do you determine whether each pair of figures is similar and justify your answer?

triangle PQR, side PR is 3 and angles P and R are both 60 degrees,

triangle GHI, side GH is 7 and angles G and H are both 60 degrees.

Both triangles must be equilateral if two angles are 60 degrees. (The third angle of each triangle must also be 60 in that case)

Since they have different side lengths, and equal angles to each other, they must be similar, but not congruent.

To determine whether each pair of figures is similar, we need to compare their corresponding sides and angles.

For triangle PQR:
- Side PR is given as 3 units.
- Angles P and R are both given as 60 degrees.

For triangle GHI:
- Side GH is given as 7 units.
- Angles G and H are both given as 60 degrees.

To check for similarity, we need to ensure that the corresponding angles are equal and the corresponding sides are proportional.

Comparing the angles:
Since the angles P and R in triangle PQR are both 60 degrees, and the angles G and H in triangle GHI are also both 60 degrees, the corresponding angles are equal. This is a good indication that the triangles could be similar.

Comparing the sides:
To check if the corresponding sides are proportional, we need to calculate the ratio of the sides PR and GH.

Ratio of PR to GH:
PR/GH = 3/7

If the ratio is the same for all the corresponding sides, then the triangles are similar. In this case, we don't have information about the corresponding sides QR and HI. Therefore, we can't determine whether the sides are proportional or not.

To conclude, based on the information given, we can say that there is a possibility that triangle PQR and triangle GHI could be similar. However, we need more information about the other sides (QR and HI) to make a definitive determination.