Congruence and congruent triangles

Lessons

• Introduction
  a)

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

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• 1.
  Which pairs of triangles are congruent?
  a)

  
  
  
  
  
  b)

  
  
  
  
  
  c)

  
  
  
  
  

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• 2.
  In the following diagram, $\triangle\ GHK$ $\cong$ $\triangle\ QRS$.
  
  i) Find.
  a)

  m$\angle\ G$ = ?
  
  
  b)

  m$\angle\ R$ = ?
  
  
  c)

  SR = ?
  
  
  d)

  $\overline{HK}$ = ?
  
  
  e)

  Find m$\angle\ R$.
  
  

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• 3.
  The gardener wants to divide a rectangular flower bed into 2 parts as shown in the following figure. Identify if the two parts are the same size and shape.
  
  

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• 4.
  Write a two-column proof.
  a)

  
  
  Given: $\overline{AC}$$\cong$$\overline{BD}$, $\overline{AD}$$\cong$$\overline{BC}$, $\angle\ CAD$$\cong$$\angle\ CBD$, $\angle\ ADC$$\cong$$\angle\ BCD$
  Prove: $\triangle\ ACD$$\cong$$\triangle\ BDC$
  
  
  b)

  Given: $\overline{XC}$$\cong$$\overline{ZC}$
  $\overline{CY}$ bisects $\overline{XZ}$
  Prove: $\triangle\ XCY$$\cong$$\triangle\ ZCY$
  
  
  
  

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• 5.
  Write a flow proof
  a)

  Given: $\overline{AC}$$\cong$$\overline{BD}$, $\overline{AD}$$\cong$$\overline{BC}$, $\angle\ CAD$$\cong$$\angle\ CBD$, $\angle\ ADC$$\cong$$\angle\ BCD$
  Prove: $\triangle\ ACD$$\cong$$\triangle\ BDC$
  
  
  
  
  b)

  Given: $\overline{XC}$$\cong$$\overline{ZC}$
  $\overline{CY}$ bisects $\overline{XZ}$
  Prove: $\triangle\ XCY$$\cong$$\triangle\ ZCY$
  
  
  
  

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