Download Section 4.2

Geometry
4-2
Big Idea: Use corresponding parts
of congruent triangles to show
triangle congruence.
Congruent Figures: have the same shape, parts
and measures.
Corresponding parts : are parts of a figure that
are related to the same parts of another figure
A
B
D
C
Corresponding angles
ÐA @ ÐD
ÐB @ ÐE
ÐC @ ÐF
E
F
Corresponding sides
AB @ DE
AC @ DF
BC @ EF
Theorem 4.3 Third Angle Theorem
If two angles of one triangle are congruent to the
two angles of another triangle, then the third
angles are also congruent.
B
A
E
C
D
F
If ÐA @ ÐD and ÐB @ ÐE then ÐC @ ÐF
Theorem 4.4 Properties of Congruent Angles
Reflexive Property of Congruent Triangles:
For any triangle ABC, DABC @ DABC
Symmetric Property of Congruent Angles:
For any triangle ABC,
if DABC @ DDEF, then DDEF @ DABC
Transitive Property of Congruent Triangles:
If DABC @ DDEF and DDEF @ DJKL, then
DABC @ DJKL
Example: Write a congruence statement
for the triangles. Identify all pairs of
congruent corresponding parts.
J
S
R
K
L
T
In the diagram, DEFG @ SPQR. Find
x and y.
8 ft
D
102
G
84
12 ft
E
68
Q
F
(2x - 4) ft
(6y + x)
P
R
S