https://file.aiquickdraw.com/mathbot/file/1729193722684mtxoiqjw.jpg

To determine whether Figure D and Figure E are congruent and describe the transformations involved, let's analyze the figures.

### Observations:
1. **Figure D** is a larger version of **Figure E**.
2. **Figure D** is positioned on the positive side of the x- and y-axes, while **Figure E** is located in the negative x-values.
3. **Similarity in shape:** Both figures maintain the same overall shape but differ in size.
   
### Possible Transformations:
- **Translation**: Moves a figure without changing its shape or size.
- **Reflection**: Flips the figure over a line, such as the x-axis or y-axis.
- **Rotation**: Turns the figure around a point.
- **Dilation**: Changes the size but keeps the shape similar.

From the image, it is clear that the two figures are **not congruent** because **Figure E is a smaller version of Figure D**. Congruence requires both the size and shape to be identical. The likely transformation here involves **dilation** (reduction) combined with **translation** (moving the figure).

### Answer to the Question:
- **Transformation 1**: Dilation
- **Transformation 2**: Translation (to move the smaller figure to its current position)
- **Are the figures congruent?**: No, the two figures are not congruent because a dilation was used, which changes the size.

Would you like a more detailed breakdown of the transformations or additional help with anything?

---

Here are 5 questions to expand your understanding:
1. What are the conditions for two figures to be congruent?
2. How is a dilation mathematically described?
3. What distinguishes congruence from similarity?
4. How do you identify a translation from a graph?
5. What is the effect of combining multiple transformations?

**Tip:** If two figures have the same shape but different sizes, they are considered **similar**, not congruent.

Understand how to determine the congruence and similarity of geometric figures using transformations. This problem involves analyzing figures for dilation, translation, and other transformations, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation