Triangles congruent by ASA and AAS proofs

Lessons

• Introduction
  a)

  1. Similar tirangles VS. Congruent triangles
  2. Ways to prove congruency:
  • SSS
  • SAS
  • ASA
  • AAS
  
  

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• 1.
  What is the third congruence that is needed to prove that $\triangle ABC$$\cong$$\triangle DEF$ using the given postulate or theorem?
  
  
  a)

  $\overline {AB}$$\cong$$\overline {DE}$ and $\angle C$$\cong$$\angle F$
  Prove by AAS.
  
  
  b)

  $\overline {AC}$$\cong$$\overline {DF}$ and $\angle A$$\cong$$\angle D$
  Prove by ASA.
  
  
  c)

  $\angle A$$\cong$$\angle D$ and $\angle B$$\cong$$\angle E$
  Prove by AAS.
  
  

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• 2.
  Decide if the following triangles are congruent. Show your reasoning.
  a)

  $\triangle ABC$, $\triangle CBD$
  
  
  
  
  b)

  $\triangle XYZ$, $\triangle XWZ$
  
  
  
  

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