Download 4-2 - Congruence and Triangles Congruent

SGeo_4­2smartnotes.notebook
January 13, 2014
4-2 - Congruence and Triangles
Goal: Identify congruent figures and corresponding parts
Prove that 2 triangles are congruent
Congruent - Same size and same shape
Corresponding angles - Angles that match up
Corresponding sides - Sides that match up
** In congruent figures corresponding angles and corresponding
sides are congruent**
http://www.mathopenref.com
Aug 28­8:23 AM
Third angle theorem If 2 angles of 1 triangle are congruent to 2
angles of another triangle, then the third
angles are also congruent
D
A
B
If A ≅
C
D and
B≅
E
E, then
F
C≅
D
Sep 8­8:49 AM
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SGeo_4­2smartnotes.notebook
January 13, 2014
Properties of congruent triangles
A
B
C
Reflexive Property - Every triangle is
congruent to itself
ΔA≅ΔA
Symmetric Property - Can change the order
If ΔA≅ΔB, then ΔB≅ΔA
Transitive Property - Can take out the
middle man
If ΔA≅ΔB and ΔB≅ΔC, then ΔA≅ΔC
Sep 8­9:06 AM
Example 1: Naming congruent parts
Identify all pairs of corresponding congruent parts
A
C
B
D
F
E
Aug 28­9:01 AM
2
SGeo_4­2smartnotes.notebook
January 13, 2014
Example 2: Using properties of congruent figures
F
In the diagram, NPLM≅EFGH
8m
M
G
L
(2x­3)m
110
(7y+9)
87
P
72
10m
E
H
N
a) Find the value of x
b) Find the value of y
Dec 19­8:53 AM
Example 3: Using the third angle theorem
Find the value of x
(2X+30)
55
65
Example 4: Determining whether triangles are congruent
Decide whether the triangles are congruent. Justify your reasoning
R
N
92
92
P
Q
M
HW: 4.2A(1-2, 4-10, 12, 14), 4.2C(6-11)
Dec 19­9:07 AM
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