4'4 Proving triangles using ASA and AAS

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4.4 Proving triangles using ASA and AAS

• p. 220

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Post 21Angle-Side-Angle (ASA) ? post

• If 2 ?s and the included side of one ? are ? to
  the corresponding ?s and included side of another
  ?, then the 2 ?s are ?.

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B
((
C
)
If ?A ? ?Z, ?C ? ?X and seg. AC ? seg. ZX, then ?
ABC ? ? ZYX.
A
Y
(
Z
))
X
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Thm 4.5Angle-Angle-Side (AAS) ? thm.

• If 2 ?s and a non-included side of one ? are ? to
  the corresponding ?s and non-included side of
  another ?, then the 2 ?s are ?.

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B
)
A

• If ?A ? ?R, ?C ? ?S, and seg AB ? seg QR, then
  ?ABC ? ?RQS.

((
C
S
))
Q
)
R
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Proof

• 1. ?A ? ?R,?C ? ?S, seg AB ? seg QR,
• 2. ?B ? ?Q
• 3. ? ABC ? ? RQS

• 1. Given
• 2. 3rd angles thm
• 3. ASA post

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ExamplesIs it possible to prove the ?s are ??
(
)
))
))
((
)
(
((
No, there is no AAA thm!
Yes, ASA
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THERE IS NO AAA (CAR INSURANCE) OR BAD WORDS
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Example

• Given that ?B ? ?C, ?D ? ?F, M is the midpoint of
  seg DF
• Prove ? BDM ? ? CFM

B
C
)
)
((
))
D
M
F
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Proof

• Statements
• 1. Given that ?B _at_ ?C, ?D _at_ ?F, M is the
  midpoint of seg DF
• 2. Seg DM _at_ Seg MF
• 3. ? BDM _at_ ? CFM

• Reasons
• 1. Given
• 2. Def of a midpoint
• 3. AAS thm

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Example

• Given that seg WZ bisects ?XZY and ?XWY
• Prove that ? WZX _at_ ? WZY

X
)
((
W
Z
((
)
Y
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Proof

• Statements
• 1. seg WZ bisects ?XZY and ?XWY
• 2. ?XZW _at_ ?YZW, ?XWZ _at_ ?YWZ
• 3. Seg ZW _at_ seg ZW
• 4. ? WZX _at_ ? WZY

• Reasons
• 1. Given
• 2. Def? bisector
• 3. Reflex prop of seg _at_
• 4. ASA post

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4.5 Using ? ?s

• Pg 229

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Once you know that ?s are ?, you can state that
their corresponding parts are ?.
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CPCTC

• CPCTC-corresponding parts of _at_ triangles are _at_.
• Ex G seg MP bisects
  ?LMN, seg LM _at_ seg NM
• P seg LP _at_ seg NP

P
N
L
)
(
M
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Proof

• Statements
• 1. Seg MP bisects ?LMN, seg LM ? seg NM
• 2. Seg PM ? seg PM
• 3. ?PMN ? ?PML
• 4. Seg LP ? seg NP

• Reasons
• Given
• Reflex. Prop seg ?
• SAS post
• CPCTC

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Assignment