Find all the congruent rectangles5552.52.52.52.52.52.52.52.52.52.52.52.5555AAABBBCCCDDDEEEFFFGGGHHHIIIJJJ33

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

Find Congruent Rectangles in a 5×2.5 Unit Grid Pattern

Q: How do I find the dimensions of each rectangle in the grid?

Use the coordinate labels and given measurements! For rectangle ABJI: length AB = 5 and width AI = 3. For rectangle BCFG: length BC = 2.5 and width BG = 6.

Q: What does it mean for rectangles to be congruent?

Congruent rectangles have exactly the same size and shape - their corresponding sides are equal. Rectangle ABJI ≅ IJGH means both have dimensions $ 5 \times 3 $.

Q: Can rectangles be congruent if they're in different positions?

Yes! Position doesn't matter for congruence. Rectangle ABGH and BDEG are congruent because both measure $ 5 \times 6 $, even though they're in different locations on the grid.

Q: How do I know which rectangles to compare?

Look for rectangles with the same calculated dimensions. Group them by size: 5×3 rectangles, 2.5×6 rectangles, and 5×6 rectangles form separate congruent sets.

Q: Why are there overlapping rectangles mentioned in the explanation?

Some rectangles share the same space on the grid but are defined by different vertex combinations. ABJI and IJGH both occupy a 5×3 area but use different corner points to define their boundaries.

Rectangle Congruence with Grid Coordinates

Find all the congruent rectangles

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Understand the problem

Find all the congruent rectangles

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.

Final Answer

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

Key Points to Remember

Essential concepts to master this topic

Congruence Rule: Rectangles are congruent when corresponding sides are equal
Grid Method: Calculate dimensions using coordinate differences: $AB = 5, AI = 3$
Verification: Check both length and width match: $5 \times 3 = 5 \times 3$ ✓

Common Mistakes

Avoid these frequent errors

Assuming rectangles that share vertices are congruent
Don't assume rectangles ABCD and EFGH are congruent just because they share some points! This ignores actual measurements. Always calculate the length and width of each rectangle using coordinate differences or given measurements to verify congruence.

Practice Quiz

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Are the rectangles congruent?

FAQ

Everything you need to know about this question

How do I find the dimensions of each rectangle in the grid?

Use the coordinate labels and given measurements! For rectangle ABJI: length AB = 5 and width AI = 3. For rectangle BCFG: length BC = 2.5 and width BG = 6.

What does it mean for rectangles to be congruent?

Congruent rectangles have exactly the same size and shape - their corresponding sides are equal. Rectangle ABJI ≅ IJGH means both have dimensions $5 \times 3$ .

Can rectangles be congruent if they're in different positions?

Yes! Position doesn't matter for congruence. Rectangle ABGH and BDEG are congruent because both measure $5 \times 6$ , even though they're in different locations on the grid.

How do I know which rectangles to compare?

Look for rectangles with the same calculated dimensions. Group them by size: 5×3 rectangles, 2.5×6 rectangles, and 5×6 rectangles form separate congruent sets.

Why are there overlapping rectangles mentioned in the explanation?

Some rectangles share the same space on the grid but are defined by different vertex combinations. ABJI and IJGH both occupy a 5×3 area but use different corner points to define their boundaries.

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