Congruent Rectangles Property: Analyzing Perimeter Equality in Rectangles A and B

Rectangle Congruence with Perimeter Properties

If rectangle A is congruent to rectangle B, the perimeter of both rectangles must be...?

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1

Understand the problem

If rectangle A is congruent to rectangle B, the perimeter of both rectangles must be...?

2

Step-by-step solution

By definition congruent rectangles are rectangles that have the same area and the same perimeter.

3

Final Answer

The same.

Key Points to Remember

Essential concepts to master this topic
  • Definition: Congruent rectangles have identical dimensions and properties
  • Technique: Use P = 2(l + w) for both rectangles
  • Check: Verify same length, width, area, and perimeter values ✓

Common Mistakes

Avoid these frequent errors
  • Confusing congruent with similar rectangles
    Don't assume congruent just means 'same shape' = wrong conclusions about perimeter! Similar rectangles have proportional sides but different perimeters. Always remember congruent means identical size and shape with exact same measurements.

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 identical in every way - they have the exact same length, width, area, and perimeter. You could place one on top of the other and they would match perfectly!

How is this different from similar rectangles?

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Similar rectangles have the same shape but different sizes. Their sides are proportional but not equal. Only congruent rectangles have identical perimeters.

Do I need to calculate the perimeter to check if it's the same?

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Not necessarily! If you know the rectangles are congruent, their perimeters must be equal by definition. The congruence tells you everything about their measurements.

Can rectangles have the same perimeter but not be congruent?

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Yes! For example, a 3×5 rectangle and a 2×6 rectangle both have perimeter 16, but they're not congruent because their dimensions are different.

What other properties are the same in congruent rectangles?

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  • Area: Identical area measurements
  • Diagonal length: Same diagonal measurements
  • Angles: All 90° angles (but this is true for all rectangles)

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