The triangles in the image are NOT similar.
To determine whether triangles are similar, we can use the following theorems:
AA Similarity: If two pairs of corresponding angles are congruent, then the triangles are similar.
SSS Similarity: If three pairs of corresponding sides are proportional, then the triangles are similar.
SAS Similarity: If two pairs of corresponding sides are proportional and the corresponding angles between them are congruent, then the triangles are similar.
In the image, we have the following information:
Triangle APRQ has sides of length 14, 35, and 25.
Triangle DHK has sides of length 21, 30, and 21.
We can see that the sides of the triangles are not proportional, so we can eliminate the SSS and SAS similarity theorems.
To check for AA similarity, we need to compare the angles of the triangles. We can see that the angles of the triangles are not congruent, so the triangles are not similar.
Therefore, the answer is:
Similarity Theorem: N/A
Similarity statement: N/A