Question

determine whether the figures are reflections of one another. if so, identify the line of reflection.
7 how do you know whether two figures are not reflections of one another?

Explanation:

Step1: Recall reflection property

In a reflection, corresponding points of the two - figures are equidistant from the line of reflection and the figures have the same shape and size but opposite orientation.

Step2: Analyze figure a

The two parallelograms in figure a have different orientations and there is no line such that corresponding points are equidistant from it. So they are not reflections of each other.

Step3: Analyze figure b

The two pentagons in figure b have the same orientation. In a reflection, the orientation should be reversed. So they are not reflections of each other.

Step4: Analyze figure c

The two triangles in figure c have the same orientation. In a reflection, the orientation should be reversed. So they are not reflections of each other.

Step5: General rule for non - reflection

If there is no line that can be drawn such that for every point on one figure, there is a corresponding point on the other figure at the same distance from the line, and the orientation is not reversed as in a reflection, the two figures are not reflections of each other. Also, if the figures have the same orientation when they should have opposite orientations in a reflection case, they are not reflections.

Answer:

a. No
b. No
c. No
For the question "How do you know whether two figures are not reflections of one another?": If there is no line of symmetry that can map one figure onto the other such that corresponding points are equidistant from the line and the orientation of one figure is not the mirror - image orientation of the other, then the two figures are not reflections of one another.