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Transcript
Congruent Polygons
To name a polygon, start at any vertex and go around the figure, either clockwise
or counterclockwise
, and name the vertices in order.
E
M
O
Example 1: Give two (out of 12) possible names for the hexagon at the right.
____________________
DEMONS
MEDSNO
____________________
D
S
N
They have the same size and shape
In simple terms, two polygons are congruent if _________________________________________________
_________________________
Their vertices can be paired so that corresponding
More formally, two polygons are congruent iff _________________________________________________
angles and sides are congruent
_______________________________________________________________________________________
Example 2. List the congruent sides and angles in the quadrilaterals below.
π‘Žπ‘›π‘”π‘™π‘’ π‘Œ
π‘Žπ‘›π‘”π‘™π‘’ 𝐺  __________
__________
E
S
G
Y __________
π‘Žπ‘›π‘”π‘™π‘’ 𝐴
π‘Žπ‘›π‘”π‘™π‘’ 𝑂  __________
π‘Žπ‘›π‘”π‘™π‘’ 𝑇
__________
π‘Žπ‘›π‘”π‘™π‘’ 𝑁  __________
π‘Žπ‘›π‘”π‘™π‘’ 𝑆
π‘Žπ‘›π‘”π‘™π‘’ 𝐸  __________
__________
O
N
T
A
𝐺𝑂
π‘Œπ΄
 __________
__________
𝑂𝑁
𝐴𝑇
 __________
__________
𝑁𝐸
𝑇𝑆
 __________
__________
𝐸𝐺
π‘†π‘Œ
 __________
__________
When naming congruent polygons, you must list the corresponding vertices in order. This is known as a
Congruent statement
____________________________________.
YATS
Example 3: Complete this congruence statement using the figure above: quad GONE  quad __________
By looking at a congruence statement, you can determine the pairs of corresponding parts.
Example 4: Use the statement  CAT   DOG to fill in the blanks.
DO
CA  _____
G
T  _____
ACT
 ODG  _____
Example 5:
V
Given: VA  VN
O is the midpoint of AN
VO  AN
VO bisects  AVN
Prove:  AVO   NVO
A
N
O
Statements
Reasons
1. ______________________________
given
1. ______________________________
π‘Žπ‘›π‘”π‘™π‘’ 𝐴 β‰… π‘Žπ‘›π‘”π‘™π‘’ 𝑁
2. ______________________________
Isosceles Triangle Thrm
2. ______________________________
𝐴𝑂 β‰… 𝑂𝑁
3. ______________________________
Def. of midpoint
3. ______________________________
Def. of perpendicular
4.π‘Žπ‘›π‘”
______________________________
𝑉𝑂𝐴 & π‘Žπ‘›π‘” 𝑉𝑂𝑁 = π‘Ÿπ‘‘. π‘Žπ‘›π‘”π‘™π‘’ 4. ______________________________
5. ______________________________
π‘Žπ‘›π‘”π‘™π‘’ 𝑉𝑂𝐴 β‰… π‘Žπ‘›π‘”π‘™π‘’ 𝑉𝑂𝑁
Right angle Thrm
5. ______________________________
6. ______________________________
π‘Žπ‘›π‘”π‘™π‘’ 𝐴𝑉𝑂 β‰… π‘Žπ‘›π‘”π‘™π‘’ 𝑁𝑉𝑂
6. ______________________________
Def. of angle bisector
𝑉𝑂 β‰… 𝑉𝑂
7. ______________________________
βˆ†π΄π‘‰π‘‚ β‰… βˆ†π‘π‘‰π‘‚
8. ______________________________
Reflexive
7. ______________________________
Def. congruent polygons
8. ______________________________