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 Practice Problems & Solutions

Master congruent rectangles with step-by-step practice problems. Learn to identify rectangles with same area and perimeter through interactive exercises.

📚Master Congruent Rectangles Through Interactive Practice

Identify congruent rectangles by comparing area and perimeter values
Calculate rectangle dimensions using given area and perimeter measurements
Solve multi-step problems involving rectangle congruence properties
Apply congruence rules to determine if two rectangles are identical
Practice with real-world examples and visual rectangle comparisons
Build confidence through progressive difficulty levels and instant feedback

Understanding Congruent Rectangles

Complete explanation with examples

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

Practice Congruent Rectangles

Test your knowledge with 2 quizzes

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?

Examples with solutions for Congruent Rectangles

Step-by-step solutions included

Exercise #1

Are the rectangles below congruent?

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

Video Solution

Exercise #2

Are the rectangles below congruent?

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:

Video Solution

Exercise #3

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

Step-by-Step Solution

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

Answer:

The same.

Video Solution

Exercise #4

Are the rectangles congruent?

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:

Video Solution

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:
$l_A + w_A = 10$ ,
$l_B + w_B = 10$ .

The identical area condition gives us:
$l_A \times w_A = l_B \times w_B$ .

Given that both the sums of $l$ and $w$ (using perimeter) and their products (using area) are equal, this enforces that $l_A = l_B$ and $w_A = w_B$ .

This implies that the rectangles are congruent (i.e., have identical lengths and widths).

Therefore, the solution to the problem is Yes.

Answer:

Yes

Frequently Asked Questions

Everything you need to know about Congruent Rectangles

What makes two rectangles congruent?

Two rectangles are congruent when they have both the same area and the same perimeter. Having only one matching property (area OR perimeter) is not sufficient for congruence.

Can rectangles with the same perimeter be congruent?

Not necessarily. Rectangles with the same perimeter are only congruent if they also have the same area. For example, a 7×5 rectangle and an 8×4 rectangle both have perimeter 24, but areas of 35 and 32 respectively, so they are not congruent.

How do I calculate if rectangles ABCD and KLMN are congruent?

Follow these steps: 1) Calculate the area of rectangle ABCD (length × width), 2) Calculate the perimeter of rectangle ABCD (2 × length + 2 × width), 3) Repeat for rectangle KLMN, 4) Compare both area and perimeter values - they must match exactly for congruence.

What's the difference between similar and congruent rectangles?

Congruent rectangles have identical area and perimeter values. Similar rectangles have the same shape (proportional sides) but can be different sizes. All congruent rectangles are similar, but not all similar rectangles are congruent.

Why do some rectangles have the same perimeter but different areas?

The perimeter depends on the sum of all sides, while area depends on the product of length and width. Different length-width combinations can produce the same perimeter but different areas, like 7×5 (P=24, A=35) versus 8×4 (P=24, A=32).

What grade level covers congruent rectangles?

Congruent rectangles are typically introduced in middle school (grades 6-8) as part of geometry units. Students learn this concept after mastering basic area and perimeter calculations for rectangles.

How can I practice congruent rectangles problems effectively?

Start with simple examples comparing two rectangles with given dimensions. Practice calculating both area and perimeter, then determine congruence. Use visual aids and work through step-by-step solutions to build understanding before attempting complex problems.

Are squares always congruent to other rectangles?

Squares are congruent to other rectangles only if both the area and perimeter match exactly. A square is a special type of rectangle, so it follows the same congruence rules: identical area AND perimeter values are required.

Continue Your Math Journey

Master Congruent Rectangles first, then advance to these related topics that build on your fraction skills

Practice by Question Type

Choose your preferred learning style and practice format for fraction problems

Identifying Congruent Rectangles

Congruent Rectangles Practice Problems & Solutions

Understanding Congruent Rectangles

Practice Congruent Rectangles

Examples with solutions for Congruent Rectangles

Frequently Asked Questions

What makes two rectangles congruent?

Can rectangles with the same perimeter be congruent?

How do I calculate if rectangles ABCD and KLMN are congruent?

What's the difference between similar and congruent rectangles?

Why do some rectangles have the same perimeter but different areas?

What grade level covers congruent rectangles?

How can I practice congruent rectangles problems effectively?

Are squares always congruent to other rectangles?

Continue Your Math Journey

Suggested Topics to Practice in Advance

Practice by Question Type