Find Congruent Rectangles in a 5×2.5 Unit Grid Pattern

Find all the congruent rectangles

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.