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
To satisfy each combination of congruences, you can use the following methods:
a. All three congruences:
To satisfy all three congruences (translation, rotation, and reflection), you can start by drawing one congruent figure on a piece of paper. Then, place tracing paper on top of it and trace the figure. Next, you can perform a translation by moving the tracing paper along a specific direction without rotating or flipping it. Finally, remove the tracing paper and reflect or rotate the original figure, making it congruent to the translated figure.
b. Translation and rotation congruences only:
To satisfy translation and rotation congruences, you can draw one congruent figure on a piece of paper. Then, choose a point on the figure to act as the center of rotation. Use a compass to draw another congruent figure by rotating it around the chosen point. Finally, you can perform a translation by moving the second figure along a specific direction without rotating it.
c. Translation and reflection congruences only:
To satisfy translation and reflection congruences, you can draw one congruent figure on a piece of paper. Then, place a mirror on the paper and reflect the figure to create another congruent figure. Finally, you can perform a translation by moving one of the figures along a specific direction without reflecting it.
d. Rotation and reflection congruences only:
To satisfy rotation and reflection congruences, you can draw one congruent figure on a piece of paper. Then, choose a point on the figure to act as the center of rotation. Use a compass to draw another congruent figure by rotating it around the chosen point. Next, place a mirror on the paper and reflect the second figure to create a third congruent figure.
e. Translation congruence only:
To satisfy translation congruence only, you can draw one congruent figure on a piece of paper. Then, perform a translation by moving the figure along a specific direction without rotating or reflecting it.
f. Rotation congruence only:
To satisfy rotation congruence only, you can draw one congruent figure on a piece of paper. Then, choose a point on the figure to act as the center of rotation. Use a compass to draw another congruent figure by rotating it around the chosen point.
g. Reflection congruence only:
To satisfy reflection congruence only, you can draw one congruent figure on a piece of paper. Then, place a mirror on the paper and reflect the figure to create another congruent figure.
h. None of the three congruences:
If none of the three congruences are required, you can simply draw one figure on a piece of paper without performing any translations, rotations, or reflections.
a. To satisfy all three congruences (translation, rotation, and reflection), you can follow these steps:
1. Start by drawing a figure on a piece of paper.
2. Take a tracing paper and place it over the figure.
3. Trace the entire figure on the tracing paper.
4. Without removing the tracing paper, flip it horizontally or vertically to create a reflection of the figure.
5. Place the tracing paper with the reflected figure on top of the original figure.
6. Slide the tracing paper to perform a translation congruence.
7. Rotate the tracing paper (with both figures) to complete a rotation congruence.
8. Now, remove the tracing paper, and you will have two congruent figures on the same piece of paper that satisfy all three congruences.
b. To satisfy translation and rotation congruences only, follow these steps:
1. Start by drawing a figure on a piece of paper.
2. Take a tracing paper and place it over the figure.
3. Trace the entire figure on the tracing paper.
4. Without removing the tracing paper, perform a translation by sliding the tracing paper in any direction.
5. Rotate the tracing paper (with the original figure) to complete a rotation congruence.
6. Now, remove the tracing paper, and you will have two congruent figures on the same piece of paper that satisfy translation and rotation congruences.
c. To satisfy translation and reflection congruences only, follow these steps:
1. Start by drawing a figure on a piece of paper.
2. Take a tracing paper and place it over the figure.
3. Trace the entire figure on the tracing paper.
4. Without removing the tracing paper, perform a translation by sliding the tracing paper in any direction.
5. Flip the tracing paper horizontally or vertically to create a reflection of the figure.
6. Place the tracing paper with the reflected figure on top of the original figure.
7. Now, remove the tracing paper, and you will have two congruent figures on the same piece of paper that satisfy translation and reflection congruences.
d. To satisfy rotation and reflection congruences only, follow these steps:
1. Start by drawing a figure on a piece of paper.
2. Take a tracing paper and place it over the figure.
3. Trace the entire figure on the tracing paper.
4. Without removing the tracing paper, rotate it to complete a rotation congruence.
5. Flip the tracing paper horizontally or vertically to create a reflection of the figure.
6. Place the tracing paper with the reflected figure on top of the original figure.
7. Now, remove the tracing paper, and you will have two congruent figures on the same piece of paper that satisfy rotation and reflection congruences.
e. To satisfy translation congruence only, follow these steps:
1. Start by drawing a figure on a piece of paper.
2. Take a tracing paper and place it over the figure.
3. Trace the entire figure on the tracing paper.
4. Without removing the tracing paper, perform a translation by sliding the tracing paper in any direction.
5. Now, remove the tracing paper, and you will have two congruent figures on the same piece of paper that satisfy translation congruence.
f. To satisfy rotation congruence only, follow these steps:
1. Start by drawing a figure on a piece of paper.
2. Take a tracing paper and place it over the figure.
3. Trace the entire figure on the tracing paper.
4. Without removing the tracing paper, rotate it to complete a rotation congruence.
5. Now, remove the tracing paper, and you will have two congruent figures on the same piece of paper that satisfy rotation congruence.
g. To satisfy reflection congruence only, follow these steps:
1. Start by drawing a figure on a piece of paper.
2. Take a tracing paper and place it over the figure.
3. Trace the entire figure on the tracing paper.
4. Without removing the tracing paper, flip it horizontally or vertically to create a reflection of the figure.
5. Place the tracing paper with the reflected figure on top of the original figure.
6. Now, remove the tracing paper, and you will have two congruent figures on the same piece of paper that satisfy reflection congruence.
h. To satisfy none of the three congruences, simply draw two different figures on the piece of paper that do not have any transformations in common.