Which of the following pairs of $\mathrm{triangles}$ can be mapped onto each other using two reflections?

• A. Two non-congruent $\mathrm{triangles}$ with no equal $\mathrm{sides}$
• B. Two congruent $\mathrm{triangles}$ that are related by a $\mathrm{rotation}$ only
• C. Two congruent $\mathrm{triangles}$ that are mirror images of each other across two intersecting $\mathrm{lines}$
• D. Two similar $\mathrm{triangles}$ with different $\mathrm{sizes}$

Answer: (C)

Verified step by step guidance

1. Understand that mapping one figure onto another using two reflections is equivalent to a rotation or a translation, depending on the lines of reflection. Specifically, two reflections across intersecting lines result in a rotation, while reflections across parallel lines result in a translation.
2. Recall that for two triangles to be mapped onto each other by reflections, they must be congruent because reflections preserve size and shape but can change orientation.
3. Analyze the options: Non-congruent triangles cannot be mapped onto each other by reflections since reflections preserve congruence; similarly, similar triangles with different sizes cannot be mapped by reflections alone because reflections do not change size.
4. Consider that two congruent triangles related by a rotation only can be obtained by two reflections across intersecting lines, since two reflections compose a rotation.
5. Conclude that the pair of triangles that can be mapped onto each other using two reflections are the two congruent triangles that are mirror images of each other across two intersecting lines.