Geometry: Congruence
Terms
AA
-
A method for proving similarity of triangles: if two angles are
congruent to their
corresponding parts in another triangle, then the triangles are similar.
AAS
-
A method for proving congruence of triangles: if two angles
and a side not
included by those angles are congruent to their corresponding parts in
another triangle, then the triangles are congruent.
ASA
-
A method for proving congruence of triangles: if two angles
and their
included side are congruent to their corresponding parts in another
triangle, then the triangles are congruent.
Congruent Triangles
-
Triangles whose corresponding angles and sides are all congruent.
Congruent Polygons
-
Polygons whose corresponding sides and interior angles are all
congruent.
Corresponding Parts
-
The angles or sides in a polygon organized such that each angle and each side
coincides with exactly one angle or side in another polygon--the pairs of angles
and sides in each polygon are called corresponding parts.
Hypotenuse-Leg
-
A method for proving congruence of
right triangles: if one
leg and the
hypotenuse are congruent to their
corresponding parts in another right triangle, the right triangles are
congruent.
SAS
-
A method for proving congruence or similarity of
triangles: if two sides
are congruent or proportional and their included angle is congruent to their
corresponding parts of another triangle, then the triangles are congruent or
similar, respectively.
Similar Triangles
-
Triangles whose corresponding angles are
congruent and whose corresponding sides are
proportional. Congruence is a subset of similarity.
SSS
-
A method for proving the congruence or similarity of
triangles: if the
three sides of a triangle are congruent to their corresponding parts, then
the triangles are congruent. If the three sides of a triangle are proportional
to their corresponding parts in another triangle, then the triangles are
similar.
