Congruent Rectangles - Examples, Exercises and Solutions

Question Types:
Congruent Rectangles: Identifying 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 ABCD and KLMN KLMN , as described in the following scheme:

Given the rectangles

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 AB=7

BC=5 BC=5

P=24 P=24

A=35 A=35

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

In the second rectangle we see the following: 

KL=8 KL=8

LM=4 LM=4

P=24 P=24

A=32 A=32

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

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

Therefore, they are not congruent.

Detailed explanation

Suggested Topics to Practice in Advance

  1. Area
  2. Rectangle
  3. Calculating the Area of a Rectangle
  4. The perimeter of the rectangle
  5. Perimeter

Practice Congruent Rectangles

Question 1

Are the rectangles congruent?

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Question 2

Are the rectangles congruent?

222333444333

Question 3

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

Question 4

Are the rectangles congruent?

222555444AAABBBDDDCCCEEEGGG

Question 5

Are the rectangles congruent?

A=20A=20A=20A=24A=24A=24

Examples with solutions for Congruent Rectangles

Exercise #1

Are the rectangles congruent?

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Video Solution

Step-by-Step Solution

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

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

8×4=32 8\times4=32

Therefore, the rectangles indeed overlap.

Answer

Yes

Exercise #2

Are the rectangles congruent?

222333444333

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

No

Exercise #3

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 #4

Are the rectangles congruent?

222555444AAABBBDDDCCCEEEGGG

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:

5×2=10 5\times2=10

The area of rectangle CDGE is equal to:

4×2=8 4\times2=8

Therefore, the rectangles do not overlap.

Answer

No

Exercise #5

Are the rectangles congruent?

A=20A=20A=20A=24A=24A=24

Video Solution

Answer

No

Question 1

Find all the congruent rectangles

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Exercise #6

Find all the congruent rectangles

5552.52.52.52.52.52.52.52.52.52.52.52.5555AAABBBCCCDDDEEEFFFGGGHHHIIIJJJ33

Video Solution

Answer

ABJI≅IJGHBCFG≅CDEFABGH≅BDEG ABJI\cong IJGH\\BCFG\cong CDEF\\ABGH\cong BDEG