Download Congruence and Triangles.notebook

Congruence and Triangles.notebook
October 19, 2015
Congruence and Triangles
triangle: a figure formed by three segments
joining three noncollinear points
A
side
C
B
vertex
Congruence and Triangles.notebook
October 19, 2015
Corresponding sides: sides of the figures that
would line up if you placed one shape on top of
the other
Corresponding angles: angles of the figures
that would line up if you placed one shape on top
of the other
Congruent figures: all of the corresponding
angles are congruent and all of the corresponding
sides are congruent
Congruence Statement: a geometric statement that says
that two figures are congruent
Y
X
Z
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
A
D
C
F
B
C
D
Find the values of the variables:
m
X
A
c°
T
30°
12
v
n
w
E
E
B
a°
B
b°
5
C
P
Congruence and Triangles.notebook
October 19, 2015
ABCDE ≅ FGHIJ
PROVING TRIANGLES ARE CONGRUENT:
SSS AND SAS
Side-Side-Side (SSS) Congruence Postulate: if 3 sides of
one triangle are congruent to 3 sides of a second triangle,
then the triangles are congruent
A
Z
X
B
Y
C
Congruence Statement:
Included Angle: the angle between 2 sides
A
C
B
Congruence and Triangles.notebook
October 19, 2015
Side-Angle-Side (SAS) Congruence Postulate: if 2 sides
and the included angle of one triangle are congruent to two
sides and the included angle of a second triangle, then the
2 triangles are congruent
O
M
J
N
L
Congruence Statement:
K
Congruence and Triangles.notebook
October 19, 2015
Is ∆ABC ≅ ∆ CDA?
A
D
C
Is ∆ABE ≅ ∆ DBC?
C
A
B
E
D
B