Congruent
From Latin: congruere  "agree, correspond with"
Definition: Equal in size and shape

Two objects are congruent if they have the same dimensions and shape. Very loosely, you can think of it as meaning 'equal', but it has a very precise meaning that you should understand completely, especially for complex shapes such as polygons.

Congruent line segments

Two line segments are congruent if they have the same length. But they need not lie at the same angle or position on the plane.
See Congruent Line Segments

Congruent angles

Two angles are congruent if they have the same measure. So if two separate angles have measures of 30° and 23° for example, they are not congruent because they have different measures. Congruent angles may lie in different orientations or positions. See Congruent Angles

Congruent circles

Two circles are congruent if they have the same size. The size can be measured as the radius, diameter or circumference. They can overlap.

Congruent polygons

Congruent polygons have an equal number of sides, and all the corresponding sides and angles are congruent. However, they can be in a different location, rotated or flipped over. So for example the two triangles shown on the right are congruent even though one is a mirror image of the other. See Congruent Polygons

Congruent polygons should not be confused with similar polygons which can be in the same proportions but different sizes.

Symbols

The symbol for congruence is congruence

If A and B are two objects being compared, such as line segments, angles, triangles etc, then the statement is read as "A is congruent to B".

If there is a diagonal line through the symbol, this means 'not': is read as "A is not congruent to B".

Pages referring to 'congruent'

Congruent triangles - Why AAA does not work
Congruent triangles - Two angles and an opposite side. AAS
Congruent triangles - Two angles and included side. ASA
Definition of a congruent angles
Definition of a congruent line segments
Four different ways to test if polygons are congruent.
Polygons are congruent when all corresponding sides and interior angles are congruent.
Definition and properties of congruent triangles - testing for congruence
Congruent triangles which share a common side.
Congruent triangles - Hypotenuse and leg of a right triangle. HL
Definition and properties of congruent triangles where one may be reflected (flipped over) with respect to the other.
Definition and properties of congruent triangles where one may be rotated with respect to the other.
Congruent triangles - Two sides and included angle. SAS
Congruent triangles - Why SSA does not work
Congruent triangles - all three sides equal. SSS