Transcript Congruence (9-5)

PRE-ALGEBRA
Congruence (9-5)
What are “congruent
figures”?
congruent figures: figures that have the same size, shape, equal sides,
and equal measures (in other words, they are exactly the same)
How do you indicate
congruent figures,
sides, and angles?
An equal sign with a wave on top (  ) is used to indicate two figures,
sides, or angles that are congruent.
Tick marks ( | || ||| ) are usually used to indicate (show) congruent
(equal) corresponding (matching) sides
Angle signs (  ) are used mark congruent (equal) angles.
Rule: Congruent figures are written in the order of congruent angles.
In other words the first letters are equal angles, second letters are equal
angles, third letters are equal angles, and so on.
Example:
PRE-ALGEBRA
Congruence (9-5)
How do you
Example: If AMN  ABC, name all of the corresponding (equal) parts and
identify congruent find MN.
parts of congruent
figures?
congruent angles: M   B,  N   C,
 MAN   BAC,  NAM   CAB
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congruent sides: MN  BC, NA  CA; MA  BA
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Since MN  BC and BC = 100 yd., then
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MN = 100 yd.
Rule: You can identify congruent (equal) triangles any of the three following
How can you
identify congruent ways.
(equal) triangles?
PRE-ALGEBRA
Congruence
LESSON 9-5
Additional Examples
In the figure,
TUV
WUX.
a. Name the corresponding congruent angles.
WUX
X, T
W , TUV
V
b. Name the corresponding congruent sides.
TV
WX , TU
WU , VU
XU
c. Find the length of WX.
Since WX,
TV, and TV = 300 m, WX = 300 m.
PRE-ALGEBRA
Examples: Write a congruency statement with the reason the following triangles
How do you
are congruent.
identify
congruent parts
of congruent
figures?
Congruence (9-5)
Example: Write a congruence statement explaining why the following triangles
are congruent.
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MN  BC
Since DFE   SFT are vertical (opposite)
angles, they are equal.
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EF  TF
DFE  SFT by Side-Angle-Side (SAS).
PRE-ALGEBRA
Congruence
LESSON 9-5
Additional Examples
List the congruent corresponding parts of each pair of
triangles. Write a congruence statement for the triangles.
a.
ACB
AC
ECD
EC
Angle
Side
CAB
CED
Angle
ACB
ECD by ASA.
PRE-ALGEBRA
Congruence
LESSON 9-5
Additional Examples
(continued)
b.
MK
MKJ
JK
MKJ
LJ
LJK
JK
Side
Angle
Side
LJK by SAS.
PRE-ALGEBRA
Congruence
LESSON 9-5
Lesson Quiz
Given that
1.
L
O
JKL
MNO, complete the following.
2. JK
MN
3. JL
MO
4. If two sides and the angle between those sides of one triangle
are congruent to two sides and the angle between those sides
of another triangle, why can you conclude that the two triangles
are congruent?
SAS
PRE-ALGEBRA