Triangles congruent by SAS and HL proofs

Lessons

• Introduction
  a)

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

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• 1.
  Write a two-column proof.
  a)

  Given: R is the midpoint of $\overline {MP}$.
  R is the midpoint of $\overline {NQ}$.
  Prove: $\triangle MRN$$\cong$$\triangle PRQ$
  
  
  
  
  b)

  Special case for right triangle:
  Given: $\triangle ABC$ is an isosceles triangle.
  D is the midpoint of $\overline {AC}$.
  Prove: $\triangle ABD$$\cong$$\triangle CBD$.
  
  
  
  

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• 2.
  Write a flow proof
  a)

  Given: R is the midpoint of $\overline {MP}$.
  R is the midpoint of $\overline {NQ}$.
  Prove: $\triangle MRN$$\cong$$\triangle PRQ$
  
  
  
  
  b)

  Special case for right triangle:
  Given: $\triangle ABC$ is an isosceles triangle.
  D is the midpoint of $\overline {AC}$.
  Prove: $\triangle ABD$$\cong$$\triangle CBD$.
  
  
  
  

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• 3.
  Is there enough information given to prove the following triangles are congruent? If so, explain your reasoning and point out the theorem or postulate you use.
  a)

  
  
  
  
  
  b)

  
  
  
  
  

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