# 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 .

# 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:

Ball:

RegionCongruent works in 2D:

Disk and Ball:

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 between two congruent regions:

The affine transformation:

Its affine matrix: