To determine which best completes the sentence "Triangles are congruent if they have the same..." we need to understand what makes triangles congruent.
1. Size: This refers to how large an object is, but doesn't specify any particular dimensions or measures. Simply saying two triangles are the same size is not sufficiently precise to establish congruence.
2. Angle measures and side lengths: Congruent triangles must have all corresponding sides of equal length and all corresponding angles of equal measure. This means that not only is the size considered in terms of the sides but also the shapes in terms of the angles between these sides.
3. Vertices and angles: Having the same vertices and angles does not necessarily give us enough information about the side lengths. Day in and day out, two triangles with the same angles and vertices could be different in size.
4. Angle measures: If two triangles only share the same angle measures, they could still have different side lengths, and hence different sizes overall. These would be similar triangles, not necessarily congruent.
Therefore, the correct answer is:
B. angle measures and side lengths
