Question

which pair of figures are a reflection of one another?

Explanation:

Step1: Recall the definition of reflection

Reflection is a transformation that flips a figure over a line. The reflected figure is congruent to the original figure and has the same shape and size, but the orientation is reversed.

Step2: Analyze the first pair of triangles

For the first pair of triangles \( \triangle A'B'C'\) and \( \triangle ABC\), we check the correspondence of vertices. If we assume a line of reflection, we can see that each vertex of \( \triangle A'B'C'\) is the mirror - image of the corresponding vertex of \( \triangle ABC\). For example, if we consider a vertical line of reflection, the position of \(A'\) with respect to \(A\), \(B'\) with respect to \(B\) and \(C'\) with respect to \(C\) follows the rule of reflection (distance from the line of reflection is the same for corresponding points).

Step3: Analyze the second pair of pentagons

For the second pair of pentagons, if we check the order of vertices. In a reflection, the order of vertices (clockwise or counter - clockwise) should be reversed. The second pair of pentagons does not follow the correct vertex - correspondence for a reflection. For example, if we start from vertex \(A\) in the first pentagon and \(A'\) in the second pentagon, the sequence of adjacent vertices \(A - B - C - F - G\) in the first pentagon and \(A' - B' - C' - F' - G'\) in the second pentagon does not show the reversed - orientation property of reflection.

Step4: Analyze the third pair of pentagons

For the third pair of pentagons, the vertex - correspondence is not consistent with the reflection rule. If we consider the relative positions of vertices like \(C\) and \(C'\), \(F\) and \(F'\) etc., they do not satisfy the condition that the line segment joining a point and its image is perpendicular to the line of reflection and bisected by it.

Answer:

The first pair of triangles (the pair where \( \triangle A'B'C'\) and \( \triangle ABC\) are shown) are a reflection of one another.