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

Start practice

Test yourself on congruent rectangles!

Are the rectangles congruent?

Practice more now

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

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 #2

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 #3

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 #4

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 #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

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

Join Over 30,000 Students Excelling in Math!

Endless Practice, Expert Guidance - Elevate Your Math Skills Today

Test your knowledge

Question 1

Are the rectangles below congruent?

Question 2

Are the rectangles below congruent?

Question 3

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

Start practice