Comparing Two Rectangles: Testing Congruence of 2×5 and 2×4 Shapes

Rectangle Congruence with Different Dimensions

Are the rectangles congruent?

222555444AAABBBDDDCCCEEEGGG

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1

Understand the problem

Are the rectangles congruent?

222555444AAABBBDDDCCCEEEGGG

2

Step-by-step solution

Note that DC divides AE into two unequal parts.

AC=5 while CE=4

The area of rectangle ABDC is equal to:

5×2=10 5\times2=10

The area of rectangle CDGE is equal to:

4×2=8 4\times2=8

Therefore, the rectangles do not overlap.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Congruent Rule: Two rectangles must have identical corresponding sides
  • Technique: Compare dimensions: Rectangle 1 is 2×5, Rectangle 2 is 2×4
  • Check: Since 5 ≠ 4, rectangles have different areas and are not congruent ✓

Common Mistakes

Avoid these frequent errors
  • Thinking rectangles are congruent if they share one dimension
    Don't assume rectangles with the same width (both 2 units) are congruent = wrong conclusion! Congruent shapes must have ALL corresponding sides equal. Always check that both length AND width match exactly.

Practice Quiz

Test your knowledge with interactive questions

Are the rectangles congruent?

A=20A=20A=20A=24A=24A=24

FAQ

Everything you need to know about this question

What does it mean for rectangles to be congruent?

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Congruent rectangles are exactly the same size and shape - they can be placed on top of each other and match perfectly. This means all corresponding sides must be equal.

Can I just compare the areas to check congruence?

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No! Different rectangles can have the same area but different shapes. For example, a 1×12 rectangle and a 3×4 rectangle both have area 12, but they're not congruent.

Do the rectangles need to be in the same position to be congruent?

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Not at all! Congruent rectangles can be rotated, flipped, or moved and still be congruent. Position doesn't matter - only the dimensions matter.

Why isn't a 2×5 rectangle the same as a 2×4 rectangle?

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Even though both have the same width of 2, their lengths are different (5 vs 4). For congruence, every corresponding side must match exactly.

How can I quickly check if two rectangles are congruent?

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  • Compare length to length and width to width
  • Both pairs must be exactly equal
  • If any dimension differs, they're not congruent

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