The statement that must be true about the two similar triangles based on the triangle similarity theorem is: option 2 and option 3.
What is the Triangle Similarity Theorem?
The triangle similarity theorem states when a segment intersects the other two sides of a triangle, and the segment is parallel to the third side, then the two triangles formed are similar, and the corresponding sides are proportional to each other.
Given that line segment BD is parallel to line segment AE, therefore, triangles CBD and CAE are similar triangles, their corresponding angles are congruent, while their corresponding sides are proportional.
Therefore, the statement that must be true about the two similar triangles based on the triangle similarity theorem is: option 2 and option 3.
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