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Let's analyze the given problem.

We are provided with the following:

- **ABDE** is a rectangle.
- We need to compare:
  - **Quantity A**: The sum of the areas of triangles **ABC** and **CDE**.
  - **Quantity B**: The area of triangle **ACE**.

### Step 1: Understanding the Geometry
Since **ABDE** is a rectangle, we can observe the following:
- The diagonal lines divide the rectangle into triangles.
- Triangles **ABC** and **CDE** share the vertex **C**, and their combined area forms a part of the area of the rectangle.
- Triangle **ACE** also shares the vertex **C** with the other two triangles, and its area is related to the area of the rectangle as well.

### Step 2: Geometric Relationships
We can use the fact that the total area of the rectangle is divided into several triangles. The key observations are:
- **Triangle ABC** and **CDE** are formed by splitting the two halves of the rectangle along the diagonal **BD** and **CE** respectively.
- **Triangle ACE** spans across both **ABC** and **CDE** since it uses vertices **A**, **C**, and **E**.

### Step 3: Area Comparison
We can infer that the area of **Triangle ACE** (Quantity B) is the same as the sum of the areas of **Triangles ABC** and **CDE** (Quantity A) because:
- Triangle **ACE** is formed by splitting **ABDE** across the diagonal **AC**.
- The two triangles **ABC** and **CDE** collectively form the exact same region covered by **ACE**.

### Conclusion:
The two quantities are equal.

Answer: **The two quantities are equal.**

Would you like further clarification on any part of the solution?

Here are 5 questions you might want to consider:
1. How can the area of a triangle be calculated in a rectangle?
2. What are the properties of diagonals in a rectangle?
3. How does the positioning of triangles affect their area in a geometric figure?
4. Could this concept be extended to other shapes, such as parallelograms?
5. What happens if the rectangle is not divided symmetrically?

**Tip:** In problems involving geometric figures, symmetry often helps in comparing areas or lengths more easily.

Compare the sum of the areas of triangles ABC and CDE with the area of triangle ACE, given that ABDE is a rectangle.

This problem compares the sum of the areas of triangles ABC and CDE with the area of triangle ACE, given that ABDE is a rectangle. The problem explores geometric relationships and the concept of congruent triangles formed by diagonals in a rectangle. Suitable for Grades 8-10.

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