Find all the congruent rectangles 5 5 5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 5 5 5 A A A B B B C C C D D D E E E F F F G G G H H H I I I J J J 3 3

$$ ABJI\cong IJGH\\BCFG\cong CDEF\\ABGH\cong BDEG $$

$$ ABJI\cong BCFG\\IJHG\cong CDEF\\ABHG\cong ADEH $$

Congruent Rectangles

Congruent rectangles are those that have the same area and the same perimeter.

Let's look at an exercise as an example:

Given the rectangles $ABCD$ and $KLMN$ , as described in the following scheme:

Observe the data that appears in the scheme and determine if they are congruent rectangles.

In the first rectangle we see the following:

$AB=7$

$BC=5$

$P=24$

$A=35$

That is, the perimeter is equal to $24$ and the area, to $35$ .

In the second rectangle we see the following:

$KL=8$

$LM=4$

$P=24$

$A=32$

That is, the perimeter is equal to $24$ and the area, to $32$ .

Both rectangles have the same perimeter, but their area is different.

Therefore, they are not congruent.

Detailed explanation

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Test yourself on congruent rectangles!

Are the rectangles below congruent?

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Exercise with Congruent Rectangles

Exercise 1

Examples and Exercises with Solutions for Congruent Rectangles

Exercise #1

Are the rectangles below congruent?

Video Solution

Step-by-Step Solution

We can see that the length is identical in both rectangles: 3=3.

However their widths are not equal, as one is 2 while the other is 4.

Therefore, the rectangles are not congruent.

Answer

Exercise #2

Are the rectangles congruent?

Video Solution

Step-by-Step Solution

To determine whether the rectangles are congruent, we need to understand what congruence means for geometric figures.

Definition of Congruent Rectangles:
Two rectangles are congruent if and only if they have exactly the same dimensions. This means they must have the same length and the same width. Congruent figures can be placed on top of each other through rigid motions (translation, rotation, reflection) and match perfectly.

Key Observation:
An important property of congruent figures is that they must have equal areas. While equal areas don't guarantee congruence for rectangles, different areas guarantee that the rectangles are NOT congruent.

Analysis of the Given Rectangles:
From the diagram, we can see:

Rectangle 1 has area $A = 24$
Rectangle 2 has area $A = 20$

Conclusion:
Since the two rectangles have different areas ( $24 \neq 20$ ), they cannot possibly have the same dimensions. Therefore, the rectangles are not congruent.