Name: _______________________________
The Concept of Congruence
Date:_______ Period:_____
Ms. Anderle
The Concept of Congruence
 Objects that are exactly the same size and shape are said to be congruent
 Congruent objects are duplicates of one another
 If two mathematical figures are congruent, you cut one figure out with a pair of scissors,
it will fit perfectly on top of the other figure
Congruent
Symbol

The mathematical symbol used to denote congruent is  .
The symbol is made up of two parts:
~ which means the same shape (similar) and
= which means the same size (equal)
When you are looking at congruent figures, be sure to find the sides and the angles that “match
up” (are in the same places) in each figure. Sides and angles that “match up” are called
corresponding sides and corresponding angles.
In congruent figures, these corresponding parts are also congruent. The corresponding sides
will be equal in measure (length) and the corresponding angles will be equal in degrees.
When triangles are congruent and one triangle is placed on top of the other, the sides and
angles that coincide (are in the same positions) are called corresponding parts.
Example:
When two triangles are congruent, there are 6
facts that are true about the triangles:
 The triangles have 3 sets of congruent
(of equal length) sides
 The triangles have 3 sets of congruent
(of equal measure) angles
NOTE: The corresponding congruent sides are
marked with small straight line segments
called hash marks.
The corresponding angles are marked with
arcs.