Download 4-1 Congruent Polygons

4.1 Congruent
Polygons
Naming & Comparing Polygons
♥ List vertices in order, either
clockwise or counterclockwise.
♥ When comparing 2 polygons,
begin at corresponding vertices;
name the vertices in order and; go
in the same direction.
♥ By doing this you can identify
corresponding parts.
D
E
C
A
B
DCBAE
I
H
J
P
<D corresponds to < I
AE corresponds to PH
K
IJKPH
Name corresponding parts
• Name all the angles that correspond:
< D corresponds to < I
< C corresponds to < J
< B corresponds to < K
< A corresponds to < P
< E corresponds to < H
I
D
H
E
C
A
B
J
P
K
DCBAE
IJKPH
• Name all the segments that correspond:
DC corresponds to IJ
CB corresponds to JK
BA corresponds to KP
AE corresponds to PH
ED corresponds to HI
How many
corresponding
angles are
there?
5
How many
corresponding
sides are there?
5
D
E
C
A
• How many ways
can you name
pentagon DCBAE?
10
B
Do it.
Pick a vertex and go clockwise
Pick a vertex and go counterclockwise
DCBAE
DEABC
CBAED
CDEAB
BAEDC
BCDEA
AEDCB
ABCDE
EDCBA
EABCD
Polygon Congruence
Postulate
If each pair of corresponding angles is
congruent, and each pair of corresponding
sides is congruent, then the two polygons
are congruent.
Congruence Statements
• Given: These polygons
are congruent.
A
B
• Remember, if they are
congruent, they are
EXACTLY the same.
D
E
C
H
G
ABCD ~
= EFGH
F
• That means that all of the
corresponding angles are
congruent and all of the
corresponding sides are
congruent.
• DO NOT say that ‘all
the sides are congruent”
and “all the angles are
congruent”, because they
are not.
Third Angles Theorem
If two angles of one triangle are congruent
to two angles of another triangle, then the
third angles are congruent
X
A
B
Y
C
Z
If
<A = <X
and
<B = <Y,
then
<C = <Z
X
You are given this
graphic and statement.
Write a 2 column proof.
Prove: ΔLXM ~
= ΔYXM
Statements
~ XL
XY =
~
LM = YM
~
XM = XM
~<Y
<L=
L
M
Y
~
< XMY = < XML
Reasons
Given
Given
Reflexive Property
Given
All right angles are
congruent
~
<LXM = < YXM
Third Angle Theorem
~ ΔYXM
ΔLXM =
Polygon Congruence
Postulate
Each pair of polygons is congruent. Find
the measures of the numbered angles.
m<1 = 110◦
m<2 = 120◦
m<5 = 140◦
m<6 = 90◦
m<8 = 90◦
m<7 = 40◦
A student says she can use the information in
the figure to prove ACB  ACD.
Is she correct? Explain.
Given:
AD and BE bisect each other.
AB  DE
A  D
Prove: ACB  DCE
Statements
Reasons
1) AD and BE bisect
1) Given
each other.
AB  DE, A  D
2) AC  CD , BC  CE 2)
3) ACB  DCE
3) Vertical angles are congruent
4) B  E
4)
5) ACB  DCE
5)
Assignment
4.1 Reteach
Worksheet