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

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

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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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 below congruent?

Video Solution

Step-by-Step Solution

Since there are two pairs of sides that are equal, they also have the same area:

$8\times4=32$

Therefore, the rectangles are congruent.

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

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

Answer

The same.

Exercise #5

Find all the congruent rectangles

Video Solution

Step-by-Step Solution

Since JI intersects AH and divides it into two identical parts, we can claim that:

$AI=IH=BJ=JG=3$

And since it is given that:

$AB=HG=5$

Rectangles ABJI and IJGH are equal and overlapping.

Let's look at rectangle ADEH where AH equals 6, therefore:

$AH=DE=6$

From this it follows that:

$AH=CF=DE=6$

It is also given that:

$BC=CD=GF=FE=2.5$

Therefore we can claim that rectangles BCFG and CDEF are equal and overlapping.

Since side BG divides sides HE and AD into two equal parts:

$AB=BD=HG=GE=5$

And since:

$AH=BG=DE=6$ we can claim that rectangles BDEG and ABGH are equal and overlapping.

Answer

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

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Question 1

Are the rectangles below congruent?

Question 2

Are the rectangles congruent?

Question 3

Are the rectangles congruent?

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