Congruent Polygons:
•Define congruent polygons
•Solve problems by using congruent polygons

Polygon Congruence: If two polygons are congruent, then their respective angles and sides are congruent. The converse is also true: If the respective angles and sides of a polygon match, then the polygons are congruent. These facts will be stated later as a postulate, but first you will need to learn some terminology and notation.

Ex 1:
What are all of the possible names for the hexagon below?

Solution:
Make an organized list. You can approach the question systematically, as follows: Pick a letter from the figure, such as A. Then write the letters of each vertex of the figure, going first in one direction and then in the other.
ABCDEF AFEDCB
Then use each of the other letters in the figure as starting points.
BCDEFA
CDEFAB
DEFABC
EFABCD
FABCDE
BAFEDC
CBAFED
DCBAFE
EDCBAF
FEDCBA

Corresponding Sides and Angles: If two polygons have the same number of sides, it is possible to set up a correspondence between them by pairing their parts. In quadrilaterals ABCD and EFGH, for example, you can pair angles A and E, B and F, C and G, and D and H. Notice that you must go in the same order around each of the polygons. The correspondence of the sides follows from the correspondence of the angles. In this case, side AB corresponds to side EF, and son on.

Ex 2:
The polygons below are congruent. Write a congruence statement about them.

Solution:
Write a name for one of the polygons, followed by the congruence symbol. Then imagine moving the other polygon on top of the first one so that they match exactly Finally, write the name of the second polygon to the right of the congruence symbol, with the corresponding vertices listed in order. ABCD = EFGH

Polygon Congruence Postulate: Two polygons are congruent if and only if there is a correspondence between their sides and angles such that:
•Each pair of corresponding angles is congruent
•Each pair of corresponding sides is congruent

Ex 3:
Prove triangle REX = triangle FEX

Solution:
List all of the sides and angles that are given to be congruent
‹R = ‹F RE = FE
‹REX = ‹FEX RX = FX
‹EXR = ‹EFX

Six congruences are required for triangles to be congruent, three pairs of angles and three pairs of sides. Thus, one more pair of congruent sides is needed for these triangles. Notice that EX is shared by the two triangles. Use the Reflexive Property of Congruence to justify the statement that EX = Ex. This gives the sixth congruence, so you can conclude that triangle REX = triangle FEX.

Triangle Congruence:
•Explore triangle rigidity
•Develop three congruence postulates for triangles, SSS, SAS, and ASA

Activity 1:
1. Construct each triangle described below from drinking straws and string. When you pull the strings tight, your triangles will be rigid.

Congruent Polygons:•Define congruent polygons

•Solve problems by using congruent polygons

Polygon Congruence: If two polygons are congruent, then their respective angles and sides are congruent. The converse is also true: If the respective angles and sides of a polygon match, then the polygons are congruent. These facts will be stated later as a postulate, but first you will need to learn some terminology and notation.

Ex 1:

What are all of the possible names for the hexagon below?

Solution:

Make an organized list. You can approach the question systematically, as follows: Pick a letter from the figure, such as A. Then write the letters of each vertex of the figure, going first in one direction and then in the other.

ABCDEF AFEDCB

Then use each of the other letters in the figure as starting points.

BCDEFA

CDEFAB

DEFABC

EFABCD

FABCDE

BAFEDC

CBAFED

DCBAFE

EDCBAF

FEDCBA

Corresponding Sides and Angles: If two polygons have the same number of sides, it is possible to set up a correspondence between them by pairing their parts. In quadrilaterals ABCD and EFGH, for example, you can pair angles A and E, B and F, C and G, and D and H. Notice that you must go in the same order around each of the polygons. The correspondence of the sides follows from the correspondence of the angles. In this case, side AB corresponds to side EF, and son on.

Ex 2:

The polygons below are congruent. Write a congruence statement about them.

Solution:

Write a name for one of the polygons, followed by the congruence symbol. Then imagine moving the other polygon on top of the first one so that they match exactly Finally, write the name of the second polygon to the right of the congruence symbol, with the corresponding vertices listed in order. ABCD = EFGH

Polygon Congruence Postulate: Two polygons are congruent if and only if there is a correspondence between their sides and angles such that:

•Each pair of corresponding angles is congruent

•Each pair of corresponding sides is congruent

Ex 3:

Prove triangle REX = triangle FEX

Solution:

List all of the sides and angles that are given to be congruent

‹R = ‹F RE = FE

‹REX = ‹FEX RX = FX

‹EXR = ‹EFX

Six congruences are required for triangles to be congruent, three pairs of angles and three pairs of sides. Thus, one more pair of congruent sides is needed for these triangles. Notice that EX is shared by the two triangles. Use the Reflexive Property of Congruence to justify the statement that EX = Ex. This gives the sixth congruence, so you can conclude that triangle REX = triangle FEX.

Triangle Congruence:•Explore triangle rigidity

•Develop three congruence postulates for triangles, SSS, SAS, and ASA

Activity 1:

1. Construct each triangle described below from drinking straws and string. When you pull the strings tight, your triangles will be rigid.