Figures that correspond under a translation, rotation, or reflection are said to be translation congruent, rotation congruent, or reflection congruent. Position two congruent figures on a piece of paper to satisfy each combination
of congruences listed. Use tracing paper, mirrors, or
GES to justify your choices.
a. All three congruences
b. Translation and rotation congruences only
c. Translation and reflection congruences only
d. Rotation and reflection congruences only
e. Translation congruence only
f. Rotation congruence only
g. Reflection congruence only
h. None of the three congruences
*Can some explain what this question is asking?*
Here is what I suggest. Draw a figure on a piece of cardboard, about the size of your hand. Cut it out.
Hold it up. Move it to the right five inches. That is translation congruence.
Hold it up, rotate it 40 degrees. That is rotational congruence.
Hold it up, rotate it so that the back now faces you. That is reflection congruence.
Now do this on paper.
This question is asking you to position congruent figures on a piece of paper to satisfy different combinations of congruences. Congruent figures are identical in shape and size, and they can be obtained from each other through translations, rotations, or reflections.
(a) To satisfy all three congruences (translation, rotation, and reflection), you would need to position the figures so that they have the same shape, size, orientation, and mirror image.
(b) For translation and rotation congruences only, you would need to position the figures so that they have the same size, shape, orientation, and are shifted to a different location.
(c) For translation and reflection congruences only, you would need to position the figures so that they have the same shape, size, orientation, and mirror image, but not necessarily the same location.
(d) For rotation and reflection congruences only, you would need to position the figures so that they have the same shape, size, mirror image, but not necessarily the same location or orientation.
(e) For translation congruence only, you would need to position the figures so that they are the same shape, size, and are shifted to a different location.
(f) For rotation congruence only, you would need to position the figures so that they have the same shape, size, and orientation.
(g) For reflection congruence only, you would need to position the figures so that they have the same shape, size, and mirror image.
(h) If none of the three congruences are satisfied, then the figures cannot be positioned in a way that satisfies any combination of congruences.
You can use different techniques such as tracing paper, mirrors, or geometric construction tools (GES) to justify your choices and show the congruences.