Congruent Triangles

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Congruent Triangles
Lesson 4.3
by Marty R., Shanon V., Vilma V.
2
Standard 5
OBJECTIVE
Use properties of congruent triangles. Prove
triangles congruent by using the definition of
congruence.
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Vocabulary
Congruent - a correspondence between their angles
and sides. Corresponding Angles - Two angles that
are formed by two lines and a transversal and
occupy corresponding positions. Corresponding
Sides - When two figures are congruent the sides
that are in corresponding positions are congruent.
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How are triangles congruent? They are congruent
when each pair of the triangles corresponding
sides are equal, or congruent, and the
corresponding angles are congruent too.
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Properties of Congruent Triangles
Reflexive Property of Congruent Triangles Every
triangle is congruent to itself. Symmetric
Property of Congruent Triangles If ?ABC ? ?DEF,
then ?DEF ??ABC. Transitive Property of Congruent
Triangles If ?ABC??DEF and ?DEF??JKL, then
?ABC??JKL.
K
L
J
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Third Angles Theorem
If two angles of one triangle, then the third
angles are also congruent. If LA?LD and LB? LE,
then LC? LF.
B
E
D
F
C
A
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Note the Triangle Sum Theorem states that all
triangles equal 180 degrees.
Using the Third Angle Theorem
Find x.
In the diagram, LN? LR and LL? LS. From the Third
Angles Theorem, you know that LM? LT. So, mLM?
mLT. From the Triangle Sum Theorem, mLM
180-50-65 60.
mLMmLT 60(2x30) 302x 15x
Third Angle Theorem
T
R
M
Substitute.
Subtract three from each side.
N
L
S
Divide each side by 2.
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Classwork
GREENBOOK/pg. 234 1-10
Homework
GREENBOOK/pg. 235 13-19