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Congruent FiguresCongruent Figures
Objective:
1) To recognize figures & their corresponding parts
Congruent PolygonsCongruent Polygons
Are the same size and the same shape.Are the same size and the same shape.Fit exactly on top of each otherFit exactly on top of each other
Have Have corresponding parts: corresponding parts:Matching sides and Matching sides and ss
You can make 3 kinds of moves so that one congruent figure can fit exactly on top of top of another
You can make 3 kinds of moves so that one congruent figure can fit exactly on top of top of another
These are called translations and are covered in chapter 9
You can make 3 kinds of moves so that one congruent figure can fit exactly on top of top of another
ΔΔQXT QXT ΔΔPHDPHD
QX QX PH PH
Naming PolygonsNaming Polygons
Order Matters!!Order Matters!!
AB C
DE S
TUW
R
ABCDE
WUTSR
AB
ED
B
D
A
WU
RS
U
S
W
Example: Example: ΔΔWYS WYS ΔΔMKVMKV
mmW = 25W = 25mmY = 55Y = 55Find mFind mVV
W
Y
S
M
K
V25
55
100
Example 2: Congruence StatementExample 2: Congruence Statement
Finish the following congruence statement:
ΔJKL Δ_ _ _
K
J
L
M
N
ΔJKL ΔNML
Proof: Th(4-1)Proof: Th(4-1)
If 2 If 2 s of one s of one ΔΔ are are to 2 to 2 s another s another ΔΔ, , then the third then the third s are also s are also ..
Given: Given: B B EE
A A DDProve: Prove: C C F F
A
B C
D
FE
Statements
1)1) B B E & E & A A DD
2)2) mmB + mB + mA + mA + mC = 180C = 180
mmE + mE + mD + mD + mF = 180F = 180
3) m3) mB + mB + mA + mA + mC = C =
mmE + mE + mD + mD + mF F
4)4) mmB + mB + mA + mA + mC = C =
mmB + mB + mA + mA + mFF
5)5) mmC = mC = mFF
6)6) C C FF
Reasons
1) Given
2) Def. of Δ
3) Trans.
4) Subs.
5) Subtr.
6) Def. of
Example Example
Proof:Proof:
Given: GC Given: GC GD GD
CN CN DN DN
Prove: Prove: ΔΔGCN GCN ΔΔGDNGDN
G
CN
D
G
ND
C
Show all of the parts are
3 sides
3 angles
given
given
reflexive
given
given
Thm 4-1
