Using Congruent triangles in Proofs

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Using Congruent triangles in Proofs

• 8.4

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CPCTC

• We have now learned how to use ASA, SSS,SAS,AAS
  and HL to prove triangles congruent. Once we know
  that triangles are congruent we can make
  conclusions about corresponding angles and sides
  because Corresponding Parts of Congruent
  Triangles are Congruent. (CPCTC)

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Example I
a
d
Given AC EC, BC DC Prove lta lte
c
e
b

• Statements
• 1) AC EC
• 2) BC Dc
• 3) lt1 lt2
• 4) ABC EDC
• 5) lta lte

• Reasons
• 1) Given
• 2) Given
• 3) Vertical lts
• 4) SAS
• 5) CPCTC

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Application

• According to legend, one of Napoleons officers
  used congruent triangles to estimate the width of
  a river. How?
• The officer stood at the riverbank and lowered
  the visor to his cap until the farthest thing he
  could see was the edge of the opposite river
  bank. He then turned and noted the spot on his
  side of the river that was in line with his eye
  and the tip of the visor. The officer then paced
  of the distance to this spot and declared that
  the distance was the width of the river.

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(No Transcript)
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Write a Proof to show Napoleon's officer was
correct

• Statements
• 1) ltEDG ltEDF
• 2) DE DE
• 3) ltDEG and ltDEF are rt. Angles
• 4) ltDEG ltDEF
• 5) DEF DEG
• 6) EF EG

• Reasons
• 1) Given
• 2) Reflexive
• 3) Given
• 4) All rt. Angles
• 5) ASA
• 6) CPCTC

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Homework

• P 429 1-12, 14, 21-26