Download Section 4.2

4.2 – Congruence and Triangles
Two figures are congruent if they have the exactly same
size and shape.
E
F
A
B
C
D
If we traced triangle ABC on top of triangle DEF, they
would match up exactly.
There is also a correspondence between the angles and
sides.
 Corresponding angles are congruent to one another
 Corresponding sides are congruent to one another
Corresponding’s: A  D, B  E, C  F
Corresponding segments: AB  DE, BC  EF, AC 
DF
Corresponding Angles
A  D
B  E
C  F
Corresponding Sides
AB  DE
BC  EF
AC  DF
 Congruent Triangles – Two triangles are congruent if and
only if there is a correspondence between the vertices
such that each pair of corresponding sides and each pair
of corresponding angles are congruent.
We write ABC  DEF
When using the notation ABC  DEF, you must list
corresponding vertices in order.
Ex. Correct: ABC  DEF
Incorrect: ABC  EDF
Theorem 4.3 (Third Angles Theorem) – If two angles of
one triangle are congruent to two angles of another triangle,
then the third angles are also congruent.
A
1
2
B
3
C
4
D
5
6
E
If  2   5 and  3   4, then  1   6
Theorem 4.4 – Properties of Reflexive Triangles
Reflexive Property of Congruent Triangles – Every triangle
is congruent to itself
Symmetric Property of Congruent Triangles –
If ▲ABC  ▲DEF, then ▲DEF  ▲ABC
Transitive Property of Congruent Triangles –
If ▲ABC  ▲DEF and ▲DEF  ▲JKL,
then ▲ABC  ▲JKL