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 about similar triangles is:
C. All triangles with at least two congruent angles are similar.
To determine which inference can be made about similar triangles, let's review the properties of similar triangles.
Similar triangles are triangles that have the same shape but may differ in size. The key properties of similar triangles are:
1. Corresponding angles are congruent: The angles in one triangle are equal to the corresponding angles in the other triangle.
2. Corresponding sides are proportional: The lengths of the sides in one triangle are in proportion to the lengths of the corresponding sides in the other triangle.
Now, let's review each option:
A. Similar triangles have at least two congruent sides.
This statement is not true for all similar triangles. While it is possible for similar triangles to have two congruent sides, this is not a requirement. Therefore, option A is incorrect.
B. Similar triangles have at least one congruent side.
This statement is also not true for all similar triangles. The requirement for similarity is that the corresponding sides are proportional, not necessarily congruent. Therefore, option B is incorrect.
C. All triangles with at least two congruent angles are similar.
This statement is true. It is a property known as the Angle-Angle (AA) similarity criterion. If two triangles have two corresponding angles that are equal, then the triangles are similar. Therefore, option C is correct.
D. All triangles with at least one congruent angle are similar.
This statement is not true. Having one congruent angle is not enough to guarantee similarity. Remember that both corresponding angles need to be congruent for similarity. Therefore, option D is incorrect.
In conclusion, the correct inference about similar triangles is:
C. All triangles with at least two congruent angles are similar.