https://file.aiquickdraw.com/mathbot/file/1726248553032rfqte21i.jpg

Let's analyze the questions from the image:

### **Left Side: Determining if Figures A and B are Congruent**

1. **Are Figure A and Figure B Congruent?**
   - Yes, the two figures appear to be congruent because they have the same shape and size.

2. **Which Transformation Will Map Figure A Onto Figure B Exactly?**
   - Let's observe the figures closely:
     - Figure B is to the right of Figure A.
     - To map Figure A onto Figure B, you need to **translate Figure A to the right by 7 units**.
   - **Answer:** "Translate Figure A to the right 7 units."

### **Right Side: Determining if Figures C and D are Congruent**

1. **Are Figure C and Figure D Congruent?**
   - Yes, Figures C and D are congruent because they are identical in shape and size.

2. **Which Transformation Will Map Figure C Onto Figure D Exactly?**
   - Observing the positions of Figures C and D:
     - Figure D is a rotated version of Figure C.
     - The figures are rotated 90 degrees clockwise about the origin.
   - **Answer:** "Rotate Figure C clockwise 90° about the origin."

Would you like further details or explanations on these answers? 

### **Related Questions:**

1. What does it mean for two figures to be congruent?
2. How can you determine the type of transformation used between two congruent figures?
3. What is the effect of rotating a figure 90° clockwise around the origin?
4. How does a translation differ from a reflection?
5. What are some other types of transformations besides rotation, reflection, and translation?

### **Tip:**
Always compare the orientation, size, and position of two figures to determine the transformation needed to map one onto the other.

Determining if figures are congruent and related by a transformation

Explore whether figures are congruent and how specific transformations like translation and rotation relate them. This resource helps middle school students understand the principles of geometric congruence and transformations through practical examples.

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