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 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

The perimeter of A is 20 cm.

The perimeter of B is also 20 cm.

The area of them is identical.

Are the rectangles congruent?

Step-by-Step Solution

To determine if the two rectangles are congruent, we start by understanding that two rectangles are congruent if they have identical lengths and widths. In this problem, both rectangles have a perimeter of 20 cm and identical areas, which suggests they could potentially be congruent.

Let's recall the formulas:
Perimeter of a rectangle: $P = 2(l + w)$
Area of a rectangle: $A = l \times w$

Given that each rectangle has a perimeter $P = 20$ , we can write:
$2(l_A + w_A) = 20$ for Rectangle A,
$2(l_B + w_B) = 20$ for Rectangle B,
which simplifies to:
$l_A + w_A = 10$ ,
$l_B + w_B = 10$ .