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RegionCongruent[reg1,reg2]

tests whether the regions reg1 and reg2 are congruent.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Basic Uses  
Special Regions  
Formula Regions  
Mesh Regions  
Derived Regions  
Applications  
Properties & Relations  
See Also
Related Guides
History
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RegionCongruent

RegionCongruent[reg1,reg2]

tests whether the regions reg1 and reg2 are congruent.

Details and Options

  • The regions reg1 and reg2 are congruent if reg2 can be obtained from reg1 by a combination of translations, rotations and reflections.
  • Typically used to test whether two regions have the same shape and size or whether one has the same shape and size as the mirror image of the other.
  • RegionCongruent[reg1,reg2] gives True if there is an affine transformation from reg1 to reg2 with matrix m satisfying TemplateBox[{m}, Transpose]=TemplateBox[{m}, Inverse].

Examples

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Basic Examples  (1)

Test whether two regions are congruent:

Scope  (10)

Basic Uses  (2)

Test whether two regions are congruent:

Show two regions are not congruent:

Special Regions  (3)

RegionCongruent works in 1D:

Point:

Ball:

InfiniteLine:

RegionCongruent works in 2D:

Disk and Ball:

Polygon:

RegionCongruent works in 3D:

Formula Regions  (1)

Compare two formula regions:

Mesh Regions  (3)

Test whether two mesh regions are congruent:

Test whether two boundary mesh regions are congruent:

Test whether a mesh region and a boundary mesh region are congruent:

In :

Derived Regions  (1)

Test whether Boolean regions are congruent:

Applications  (3)

Two disks with the same radius are congruent:

Two rectangles with the same width and height are congruent:

Two polygons with the same vertex angles and edge lengths are congruent:

Properties & Relations  (3)

RegionSimilar returns True for congruent regions:

Regions that are similar are not always congruent:

Two equal regions are congruent:

FindRegionTransform gives an affine transformation m of the form TemplateBox[{m}, Transpose]=TemplateBox[{m}, Inverse] between two congruent regions:

The affine transformation:

Its affine matrix:

Wolfram Research (2021), RegionCongruent, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionCongruent.html.

Text

Wolfram Research (2021), RegionCongruent, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionCongruent.html.

CMS

Wolfram Language. 2021. "RegionCongruent." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RegionCongruent.html.

APA

Wolfram Language. (2021). RegionCongruent. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RegionCongruent.html

BibTeX

@misc{reference.wolfram_2025_regioncongruent, author="Wolfram Research", title="{RegionCongruent}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/RegionCongruent.html}", note=[Accessed: 15-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_regioncongruent, organization={Wolfram Research}, title={RegionCongruent}, year={2021}, url={https://reference.wolfram.com/language/ref/RegionCongruent.html}, note=[Accessed: 15-August-2025]}