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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Exercise with Congruent Rectangles

Exercise 1

Examples and Exercises with Solutions for Congruent Rectangles

Exercise #1

Are the rectangles congruent?

Video Solution

Step-by-Step Solution

It can be noticed that the length is identical in both rectangles: 3=3

But the width is not equal 2 is not equal to 4

Therefore, the rectangles do not overlap

Answer

Exercise #2

Are the rectangles congruent?

Video Solution

Step-by-Step Solution

Since there are two pairs of sides that are equal in size:

$4=4,8=8$ they also have the same area:

$8\times4=32$

Therefore, the rectangles indeed overlap.

Answer

Yes

Exercise #3

Are the rectangles congruent?

Video Solution

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:

$5\times2=10$

The area of rectangle CDGE is equal to:

$4\times2=8$

Therefore, the rectangles do not overlap.

Answer

Exercise #4

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

Video Solution

Step-by-Step Solution

According to the law: Congruent rectangles are rectangles that have the same area and the same perimeter.

Answer

The same.

Exercise #5

Are the rectangles congruent?

Video Solution

Answer

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Question 1

Are the rectangles congruent?

Question 2

Are the rectangles congruent?

Question 3

Are the rectangles congruent?

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