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§ 4.1 Congruent § 4.1 Congruent Figures Figures Obj: Identify ways to Obj: Identify ways to prove triangles are prove triangles are congruent. congruent.

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Page 1: congruent figures

§ 4.1 Congruent Figures§ 4.1 Congruent Figures

Obj: Identify ways to prove triangles Obj: Identify ways to prove triangles are congruent.are congruent.

Page 2: congruent figures

Congruent FiguresCongruent Figures Figures that have the same size and shapeFigures that have the same size and shape

Congruent TrianglesCongruent Triangles

Page 3: congruent figures

Parts of Congruent TrianglesParts of Congruent Triangles Corresponding AnglesCorresponding Angles

Corresponding SidesCorresponding Sides

Congruent TrianglesCongruent Triangles corresponding parts are congruentcorresponding parts are congruent

Page 4: congruent figures

Naming Triangles

A

C

B E

D

F

•Must name corresponding vertices and corresponding angles in the same order.

•**Congruence Statement**

Page 5: congruent figures

Example 1Example 1 ABC ABC XYZ. Name all the congruent XYZ. Name all the congruent

angles and congruent sides.angles and congruent sides.

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Warm Up 11/4/09 #8Warm Up 11/4/09 #8

9

15

15

x

25

Find the value of x.1. 80

2. 453. 534. 11

5. 5 6. 6

7. 418. 30

Page 7: congruent figures

§ 4.2 Proving Triangles § 4.2 Proving Triangles CongruentCongruent

Page 8: congruent figures

SSS SSS 3 pairs of congruent sides3 pairs of congruent sides

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Name the Congruent TrianglesName the Congruent Triangles

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Included AngleIncluded Angle

X

Y

Z

Given sides XY and XZ, which is the included angle?

Page 11: congruent figures

SASSAS Two pairs of congruent sides AND the Two pairs of congruent sides AND the

includedincluded angle angle

Page 12: congruent figures

Included SideIncluded Side

RP

QGiven angles Q and R, which is the included side?

Page 13: congruent figures

ASAASA 2 pairs of congruent angles AND the 2 pairs of congruent angles AND the includedincluded

side.side.

Page 14: congruent figures

Example: In which pair of triangles Example: In which pair of triangles pictured below could you use the pictured below could you use the

ASA to prove the triangles are ASA to prove the triangles are congruent?congruent?

Page 15: congruent figures

AASAAS Two pairs of congruent angles AND the Two pairs of congruent angles AND the non-non-

includedincluded side. side.

Page 16: congruent figures

HLHL Hypotenuse-LegHypotenuse-Leg Only for right triangles!Only for right triangles!

Page 17: congruent figures

ExampleExample

For each of the following, determine whether or For each of the following, determine whether or not the triangles are congruent. not the triangles are congruent. Then, write a Then, write a congruence statement and the reasoncongruence statement and the reason..

A)A) A A EEB B DD

C

A B D E

F

Page 18: congruent figures

Take another look…Take another look…

C

A B D E

FA) A E

B D

What about the other two angles? What can we say about angles C and F?

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B) B)

A

D

C

B

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C) AB C) AB CD CD

E

B

A

C

D

Page 21: congruent figures

D) D) A A EE

A

B

C

F

D

E

Page 22: congruent figures

E) E) C C EE

AC

B

DE

F