congruent figures
DESCRIPTION
proving congruent trianglesTRANSCRIPT
§ 4.1 Congruent Figures§ 4.1 Congruent Figures
Obj: Identify ways to prove triangles Obj: Identify ways to prove triangles are congruent.are congruent.
Congruent FiguresCongruent Figures Figures that have the same size and shapeFigures that have the same size and shape
Congruent TrianglesCongruent Triangles
Parts of Congruent TrianglesParts of Congruent Triangles Corresponding AnglesCorresponding Angles
Corresponding SidesCorresponding Sides
Congruent TrianglesCongruent Triangles corresponding parts are congruentcorresponding parts are congruent
Naming Triangles
A
C
B E
D
F
•Must name corresponding vertices and corresponding angles in the same order.
•**Congruence Statement**
Example 1Example 1 ABC ABC XYZ. Name all the congruent XYZ. Name all the congruent
angles and congruent sides.angles and congruent sides.
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
§ 4.2 Proving Triangles § 4.2 Proving Triangles CongruentCongruent
SSS SSS 3 pairs of congruent sides3 pairs of congruent sides
Name the Congruent TrianglesName the Congruent Triangles
Included AngleIncluded Angle
X
Y
Z
Given sides XY and XZ, which is the included angle?
SASSAS Two pairs of congruent sides AND the Two pairs of congruent sides AND the
includedincluded angle angle
Included SideIncluded Side
RP
QGiven angles Q and R, which is the included side?
ASAASA 2 pairs of congruent angles AND the 2 pairs of congruent angles AND the includedincluded
side.side.
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?
AASAAS Two pairs of congruent angles AND the Two pairs of congruent angles AND the non-non-
includedincluded side. side.
HLHL Hypotenuse-LegHypotenuse-Leg Only for right triangles!Only for right triangles!
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
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?
B) B)
A
D
C
B
C) AB C) AB CD CD
E
B
A
C
D
D) D) A A EE
A
B
C
F
D
E
E) E) C C EE
AC
B
DE
F