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
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".
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
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