1. 4.1 Congruent Polygons

2. Naming & Comparing PolygonsD C B E
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.
DCBAE P I J K H
<D corresponds to < I
AE corresponds to PH
IJKPH

3. Name corresponding parts
Name all the angles that correspond: P I J K H A D C B E
< D corresponds to < I
< C corresponds to < J
< B corresponds to < K
< A corresponds to < P
< E corresponds to < H
DCBAE
IJKPH
Name all the segments that correspond:
How many corresponding sides are there?
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 5

4. How many ways can you name pentagon DCBAE?10
Do it.
Pick a vertex and go clockwise
Pick a vertex and go counterclockwise
DEABC
CDEAB
BCDEA
ABCDE
EABCD
DCBAE
CBAED
BAEDC
AEDCB
EDCBA

5. 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.

6. Congruence Statements
Given: These polygons are congruent.
Remember, if they are congruent, they are EXACTLY the same.
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. C D B A G H F E
CONGRUENCE STATEMENT
ABCD = EFGH ~

7. 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 If
<A = <X
and
<B = <Y,
then
<C = <Z Y B Z C

8. ~ Prove: ΔLXM = ΔYXM You are given this graphic and statement.
Write a 2 column proof. X ~
Prove: ΔLXM = ΔYXM
Statements Reasons
XY = XL
LM = YM
XM = XM
< L = < Y
< XMY = < XML
<LXM = < YXM
ΔLXM = ΔYXM ~
Given ~
Given ~
Reflexive Property ~
Given L Y ~ M
All right angles are congruent ~
Third Angle Theorem
Polygon Congruence Postulate ~

9. Each pair of polygons is congruent
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◦

10. A student says she can use the information in the figure to prove ACB  ACD.
Is she correct? Explain.

11. Definition of a bisector
Given:
bisect each other.
and 
A  D
Prove: ACB  DCE
Statements
Reasons
1) AD and BE bisect each other.
AB  DE, A  D
1) Given
2) AC  CD , BC  CE 2)
3) ACB  DCE 3)
4) B  E 4)
5) ACB  DCE 5)
Definition of a bisector
Vertical angles are congruent
Third Angles Theorem
Polygon Congruence
Postulate

12. Assignment
4.1 Reteach Worksheet
4.1 Practice Worksheet