1. Corresponding Parts of Geometric Figures

2. Naming Figures
To name a polygon, write the vertices in consecutive order. For example, you can name polygon PQRS as QRSP or SRQP, but not as PRQS.
In a congruence statement, the order of the vertices indicates the corresponding parts.

3. 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

4. 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

5. 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

6. 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.

7. 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 ~

8. Examples

9. Helpful Hint
When you write a statement such as ABC  DEF, you are also stating which parts are congruent.

10. Naming Congruent corresponding Parts
Given: ∆PQR  ∆STW
Identify all pairs of corresponding congruent parts.
Angles: P  __, Q  __, R  __ S T W
Sides: PQ  __, QR  __, PR  __ ST TW SW

11. More Practice
1. ∆ABC  ∆JKL and AB = 2x JK = 4x – 50. Find x and AB.
Given that polygon MNOP  polygon QRST, identify the congruent corresponding part.
2. NO  ____ T  ____
4. ∆ABC  ∆EDC
A  __, AB  __ B  __, BC  __
C  __, AC  __
31, 74 RS P E ED D DC C EC

12. Similar Polygons
Corresponding parts must also be written in order for similar polygons.
Following the order of the statement allows you to set up proportions to solve for missing parts.

13. What do you notice about the sides of the above triangles?
Practice
What do you notice about the sides of the above triangles?

14. The “ ~ ” is used to show similarity
More Similar Polygons
Correspondence between two polygons
Corresponding angles are congruent
Lengths of the sides of the polygon are proportional
The “ ~ ” is used to show similarity
List all of the pairs of the congruent angles.

15. Writing Proportions using Corresponding Parts30 16 B C 10 D E

16. What is the scale factor?
What is a scale factor
If two polygons are similar, then the ratio of the lengths of two corresponding sides is called the scale factor. Q 6 R X 4 Y 10 15 W B P S
What is the scale factor?

17. Analysis of two Similar figures
Statement of proportionality
is called the scale factor

18. Example 10 K J Q Z P 15 6 M L R S
Quadrilateral JKLM is similar to quadrilateral PQRS. Find the value of Z

19. Complete Worksheet
Assignment