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§ 4.1 Congruent Figures§ 4.1 Congruent Figures
Obj: Identify ways to prove triangles Obj: Identify ways to prove triangles are congruent.are congruent.
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Congruent FiguresCongruent Figures Figures that have the same size and shapeFigures that have the same size and shape
Congruent TrianglesCongruent Triangles
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Parts of Congruent TrianglesParts of Congruent Triangles Corresponding AnglesCorresponding Angles
Corresponding SidesCorresponding Sides
Congruent TrianglesCongruent Triangles corresponding parts are congruentcorresponding parts are congruent
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Naming Triangles
A
C
B E
D
F
•Must name corresponding vertices and corresponding angles in the same order.
•**Congruence Statement**
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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
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§ 4.2 Proving Triangles § 4.2 Proving Triangles CongruentCongruent
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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?
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SASSAS Two pairs of congruent sides AND the Two pairs of congruent sides AND the
includedincluded angle angle
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Included SideIncluded Side
RP
QGiven angles Q and R, which is the included side?
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ASAASA 2 pairs of congruent angles AND the 2 pairs of congruent angles AND the includedincluded
side.side.
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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?
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AASAAS Two pairs of congruent angles AND the Two pairs of congruent angles AND the non-non-
includedincluded side. side.
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HLHL Hypotenuse-LegHypotenuse-Leg Only for right triangles!Only for right triangles!
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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
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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
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D) D) A A EE
A
B
C
F
D
E
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E) E) C C EE
AC
B
DE
F