Download Geometry 4-3 Congruent Triangles

Geometry 4-3 Congruent Triangles
If two or more geometric figures are exactly the same size
and the same shape, they are called congruent
.
In congruent polygons, all of the parts of one polygon are
congruent to the corresponding parts
of the other
polygon.
Show that the triangles are congruent by identifying all
congruent corresponding parts. Then write a congruence
statement.
P
X
X~
=
Z
P
XY ~
= PQ
XYZ ~
=
Given ABC~
= DFE, find the values of x and y.
D
B
54
45
2y + x
32.1 99 36
A
8y - 5
F
C 38.4
E
8y - 5 = 99
8y = 104
y = 13
2y + x = 54
2(13) + x = 54
26 + x = 54
x = 28
Theorem 4.4 - Properties of Triangle Congruence: The
Reflexive, Symmetric, and Transitive Properties of Equality
also hold true for congruence.
ABC ~
= ABC
If ABC~
= EFG, then EFG~
= ABC.
If ABC ~
= EFG and EFG~
= JKL, then ABC~
= JKL.
Y
Y~
=
R
Q
R~
= Z
YZ ~
= QR
RP ~
= ZX
Q
PQR
Theorem 4.3 - Third Angles Theorem: If two angles of one
triangle are congruent to two angles of a second triangle, then
the third angles of the two triangles are also congruent.
G
E
Given: DE~
=GE, DF~
=GF, D~
= G, DFE~
= GFE
Prove: DEF~
= GEF
D
F
Statements
Reasons
1. DE~
1. Given
=GE, DF~
=GF,
D~
= G, DFE~
= GFE
2. Reflexive
2. EF ~
= EF
3. DEF~
3. Third Angle Theorem
= GEF
4. DEF~
4. Def'n ~
= GEF
= 's