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Proving Triangles are Congruent Part One.notebook
December 05, 2013
Warm-up
List what else that would need to be congruent in order to
prove the two triangle are congruent in the given picture
because of the given postulate.
D
A
B
C
F
E
1) SAS ________________
2) SSS ________________
3) HL _________________
Y
Q
P
R
X
Z
4) SAS ___________
5) ASA ___________
6) AAS ___________
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Proving Triangles are Congruent Part One.notebook
December 05, 2013
C
B
A
D
Using only the markings above, is ∆ACD ≅∆BCD?
Mark other congruent angles or sides on the picture you can figure out by
looking at it. Do you know enough information to say the triangles are
congruent?
What if you were given the following information.
"CD bisects <ACB". Would this information tell you that other angles or sides
in the picture were congruent? If so, mark them.
Is this enough information to say the triangles are congruent? ______ Why
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Proving Triangles are Congruent Part One.notebook
December 05, 2013
In order to prove triangles are congruent,
we must use
1) Congruent angles or sides that are
given to us in the picture.
2) Congruent angles or sides we can
figure out from the picture.
3) Congruent angles or sides we can
determine from given information not
obvious from the picture.
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Proving Triangles are Congruent Part One.notebook
December 05, 2013
Information we might be given and the reasons we
could use to say we had congruent segments
Ex.
RS bisects ST
T is the midpoint of LM
Definition of a segment bisector
Definition of a midpoint
Information we can figure out in a picture and
the reason we would use for it in a proof
Common side
Common angle
Vertical Angles
Reflexive property
Reflexive property
Vertical angle Theorem
Information we might be given and the reasons
we could use to say we had congruent angles
Ex.
RS bisects <LRT
AB is parallel to CD
LM is perpendicular to ST
<A and <B are right angles
Definition of an Angle Bisector
Corresponding Angle Postulate
Alternate Interior Angle Theorem
Definition of Perpendicular lines
Right Angle Theorem
There are others for angles but these are the major one.
Please review these, as you will need to know them to write proofs of
congruent triangles.
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Proving Triangles are Congruent Part One.notebook
December 05, 2013
Classwork - Identifying Congruent
triangles from given information
With someone sitting next to you
1) Mark the items you can determine to be congruent in the
picture by looking at it.
2) Mark the items you can determine to be congruent in the
picture by using the given information
3) State whether the triangles are congruent or not
4) If they are congruent, state the congruence postulate that
justifies it.
5) If the triangle were congruent, write a congruence statement
Given: BD bisects AC
Congruent? YES or NO
Congruence Postulate _____________
Congruence Statement_____________
B
1)
A
C
D
B
2)
Given: BD is perp. to AC
Congruent? YES or NO
Congruence Postulate _____________
Congruence Statement_____________
A
C
D
B
Given: BD bisects < ABC
Congruent? YES or NO
Congruence Postulate _____________
Congruence Statement_____________
3)
A
C
D
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Proving Triangles are Congruent Part One.notebook
December 05, 2013
4)
B
Given: BD is perp. to AC, BD bisects <ABC
Congruent? YES or NO
Congruence Postulate _____________
Congruence Statement_____________
A
C
D
5)
U
R
Given: RV bisects SU
Congruent? YES or NO
Congruence Postulate _____________
Congruence Statement_____________
T
S
6)
V
U
R
Given: T is the m.p. of RV and SU
Congruent? YES or NO
Congruence Postulate _____________
Congruence Statement_____________
T
S
V
U
7) R
Given: RS is parallel to UV
Congruent? YES or NO
Congruence Postulate _____________
Congruence Statement_____________
T
S
V
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Proving Triangles are Congruent Part One.notebook
December 05, 2013
8)
U
R
Given: RV and SU bisect each other
Congruent? YES or NO
Congruence Postulate _____________
Congruence Statement_____________
T
S
V
X
9)
W
Y
Given: XZ bisects <WXY and <WZY
Congruent? YES or NO
Congruence Postulate _____________
Congruence Statement_____________
Z
10)
X
Given: WX is parallel to YZ
Congruent? YES or NO
Congruence Postulate _____________
Congruence Statement_____________
W
Y
Z
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Proving Triangles are Congruent Part One.notebook
December 05, 2013
theorem
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