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.