triangle congruence

1. Chapter 4
Congruent Triangles
Sec. 4 – 1
Congruent Figures
Objective:
1) To recognize  figures & their
corresponding parts

2. Congruent Polygons
 Are the same size and the same shape.
 Fit exactly on top of each other
 Have  corresponding parts:
 Matching sides and s

3. You can make 3 kinds of moves so
that one congruent figure can fit
exactly on top of top of another

4. 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

5. You can make 3 kinds of moves so
that one congruent figure can fit
exactly on top of top of another

8. ΔQXT  ΔPHD
QX  PH

9. Naming Polygons
 Order Matters!!
A
B C
D
E S
T
U
W
R
ABCDE  WUTSR
AB 
ED 
B 
D 
A 
WU
RS
U
S
W

10. Example: ΔWYS  ΔMKV
 mW = 25
 mY = 55
 Find mV
W
Y
S
M
K
V
25
55
100

11. Example 2: Congruence
Statement
Finish the following congruence statement:
ΔJKL  Δ_ _ _
K
J
L
M
N
ΔJKL  ΔNML

12. Proof: Th(4-1)
 If 2 s of one Δ are  to 2 s another Δ,
then the third s are also .
 Given: B  E
A  D
 Prove: C  F
A
B C
D
F
E

13. Statements
1) B  E & A  D
2) mB + mA + mC = 180
mE + mD + mF = 180
3) mB + mA + mC =
mE + mD + mF
4) mB + mA + mC =
mB + mA + mF
5) mC = mF
6) C  F
Reasons
1) Given
2) Def. of Δ
3) Trans.
4) Subs.
5) Subtr.
6) Def. of 

14. Example
 Proof:
Given: GC  GD
CN  DN
Prove: ΔGCN  ΔGDN
G
C
N
D

15. G
N
D
C
Show all of the parts are 
3 sides
3 angles
given
given
reflexive
given
given
Thm 4-1