If $\mathrm{angle}2$ is congruent to $\mathrm{angle}6$ in two right triangles, which of the following statements is true about the ratios of their corresponding sides?

• A. The ratios of the lengths of the sides opposite $\mathrm{angle}2$ and $\mathrm{angle}6$ are equal in both triangles.
• B. The ratios of the sides adjacent to $\mathrm{angle}2$ and $\mathrm{angle}6$ are always different.
• C. The triangles must be congruent.
• D. The hypotenuses of both triangles must be equal.

Answer: (A)

Verified step by step guidance

1. Recognize that if two angles (angle 2 and angle 6) in two right triangles are congruent, then the triangles are similar by the Angle-Angle (AA) similarity postulate.
2. Recall that similar triangles have corresponding angles equal and their corresponding sides are proportional, meaning the ratios of corresponding sides are equal.
3. Identify the sides relative to the given angles: the side opposite the angle, the side adjacent to the angle, and the hypotenuse.
4. Understand that because the triangles are similar, the ratio of the lengths of the sides opposite angle 2 and angle 6 will be equal, as will the ratios of the sides adjacent to these angles and the hypotenuses.
5. Conclude that the correct statement is that the ratios of the lengths of the sides opposite angle 2 and angle 6 are equal in both triangles, while the triangles do not necessarily have equal hypotenuses or must be congruent.