which of these triangle pairs can be mapped to each other using two reflections?
which of these triangle pairs can be mapped to each other using two reflections?
Answer
Explanation:
Step1: Recall reflection property
Two reflections over two intersecting lines is equivalent to a rotation. For two triangles to be mapped to each other by two reflections, they must be congruent. In the given figure, we can analyze the congruence of (\triangle XYZ) and (\triangle PYT). We know that (\angle Z = \angle T), (YZ=YT) and (\angle XYZ=\angle PYT = 90^{\circ}). By the Angle - Side - Angle (ASA) congruence criterion, (\triangle XYZ\cong\triangle PYT).
Step2: Consider reflection mapping
If we first reflect (\triangle XYZ) over the line (XY) and then over the line (YT), we can map (\triangle XYZ) onto (\triangle PYT).
Answer:
The triangle pair (\triangle XYZ) and (\triangle PYT) can be mapped to each other using two reflections.