Test Questions: Describing Mapping Sequences for Congruent Figures

📚 Quick Study Guide

• 📐 Congruent Figures: Figures that have the same size and shape.
• 🔄 Transformations: Operations that change the position or orientation of a figure. Common transformations include:
• ➡️ Translation: Slides a figure along a straight line.
• refletir Reflection: Flips a figure over a line (the line of reflection).
• rotate Rotation: Turns a figure around a point (the center of rotation).
• 📈 Dilation: Changes the size of a figure by a scale factor (not a congruence transformation unless the scale factor is 1).
• 🗺️ Mapping Sequence: A series of transformations that map one figure onto another. For congruent figures, a mapping sequence involves only translations, reflections, and rotations.
• 🎯 Goal: To describe the specific transformations needed to show that two figures are congruent.
• 💡 Key Idea: If a sequence of translations, reflections, and rotations maps one figure exactly onto another, then the figures are congruent.

Practice Quiz

1. What type of transformation changes the size of a figure?
1. Translation
2. Reflection
3. Rotation
4. Dilation
2. Which sequence of transformations proves congruence?
1. Translation, Dilation
2. Reflection, Dilation
3. Rotation, Dilation
4. Translation, Reflection, Rotation
3. A triangle is reflected over the x-axis and then translated 3 units to the right. Which statement is true?
1. The image is congruent to the original triangle.
2. The image is similar but not congruent to the original triangle.
3. The image is larger than the original triangle.
4. The image is smaller than the original triangle.
4. Which transformation does NOT preserve congruence?
1. Rotation
2. Reflection
3. Translation
4. Dilation
5. Figure A is mapped onto Figure B by a rotation of 90 degrees clockwise about the origin. What can be concluded?
1. Figure A and Figure B are similar but not necessarily congruent.
2. Figure A and Figure B are congruent.
3. Figure A is larger than Figure B.
4. Figure A is smaller than Figure B.
6. A square is translated 5 units up and 2 units to the left. What property of the square changes?
1. Side length
2. Angle measure
3. Area
4. Position
7. Two figures are congruent. Figure 1 is reflected over the y-axis to create Figure 2. Figure 2 is then rotated 180 degrees about the origin to create Figure 3. Which figure is congruent to Figure 1?
1. Figure 2 only
2. Figure 3 only
3. Both Figure 2 and Figure 3
4. Neither Figure 2 nor Figure 3