November 14, 2014
3=
5
m 1 + m 2 + m 3 = 180o
m 3=m 5
m 1+m 2=m
m 1+m 2+m
6+m
7
m 5 + m 6 + m 7 = 180o
3=m 5+m
6+m 7
November 14, 2014
(4.3) Congruent Triangles
Objective: To name and use corresponding parts of congruent
polygons.
To prove triangles congruent by the definition of
congruent triangles.
Why: Objects are often mass produced and the shape and size
must be the same.
November 14, 2014
A
Q
B
C
F
E
S
V
D
R
U
T
November 14, 2014
Obj: To name and use corresponding parts of congruent
polygons.
To prove triangles congruent by the definition of
congruent triangles.
Congruent Figures: figures with the same size and shape.
Congruent Polygons: If all of the corresponding parts (angles and
sides) are congruent, then the polygons are congruent.
November 14, 2014
DEFG = RSTU. Name all the corresponding = parts.
November 14, 2014
Obj: To name and use corresponding parts of congruent
polygons.
A
9
91
B
o
To prove triangles congruent by the definition of
congruent triangles.
L
K
4x-3
(5y-12)o
113o
86o
D
6
C
H
J
ABCD = KJHL
x = _______
y = ________
November 14, 2014
Obj: To name and use corresponding parts of congruent
polygons.
Are the triangles congruent?
1.
To prove triangles congruent by the definition of
congruent triangles.
D
A
C
B
E
November 14, 2014
Obj: To name and use corresponding parts of congruent
polygons.
To prove triangles congruent by the definition of
congruent triangles.
Third Angles Theorem:
If two angles of one triangle are congruent to two angles of
another triangle, then the third angles are congruent.
Proof:
Given:
Prove:
A
A =
X
B =
Y
C =
Z
Statement
X
B
Reason
C
Y
Z
November 14, 2014
Obj: To name and use corresponding parts of congruent
polygons.
To prove triangles congruent by the definition of
congruent triangles.
Given: MN = PQ
N
M
MN ll PQ
O
O is the midpt. of MQ and PN
Prove:
MNO =
QPO
P
Statement
Reason
Q
November 14, 2014
Obj: To name and use corresponding parts of congruent
polygons.
To prove triangles congruent by the definition of
congruent triangles.
November 14, 2014
Obj: To name and use corresponding parts of congruent
polygons.
HW:
HR:
To prove triangles congruent by the definition of
congruent triangles.
(4.3)Pg.259: 13-16, 19, 23, 29, 39, 42
November 14, 2014
Obj: To name and use corresponding parts of congruent
polygons.
To prove triangles congruent by the definition of
congruent triangles.