Which inference can be made about similar triangles?
A.
Similar triangles have at least two congruent sides.
B.
Similar triangles have at least one congruent side.
C.
All triangles with at least two congruent angles are similar.
D.
All triangles with at least one congruent angle are similar.
C. All triangles with at least two congruent angles are similar.
The correct inference that can be made about similar triangles is:
A. Similar triangles have at least two congruent sides.
The correct inference that can be made about similar triangles is option C: All triangles with at least two congruent angles are similar.
To understand why this is the case, it is helpful to know the definition of similar triangles. Two triangles are considered similar if their corresponding angles are congruent and the ratios of their corresponding sides are equal.
Option A - Similar triangles have at least two congruent sides:
This statement is not always true. While it is possible for similar triangles to have at least two congruent sides, it is not a requirement. Two triangles can have different side lengths and still be similar as long as their corresponding angles are congruent.
Option B - Similar triangles have at least one congruent side:
This statement is also not always true. Two triangles can have different side lengths and still be similar if their corresponding angles are congruent. Having at least one congruent side is not a necessary condition for similarity.
Option D - All triangles with at least one congruent angle are similar:
This statement is incorrect. Having at least one congruent angle does not guarantee similarity. It is possible for two triangles to have one congruent angle but different side lengths, meaning they would not be similar.
Therefore, the correct inference is option C: All triangles with at least two congruent angles are similar. This is because when two triangles have at least two congruent angles, their third angles must also be congruent, and the ratios of their corresponding sides will be equal, fulfilling the criteria for similarity.