Congruence and congruent triangles

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Intros
Lessons
    1. Similar tirangles VS. Congruent triangles
    2. Ways to prove congruency:
      • SSS
      • SAS
      • ASA
      • AAS
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Examples
Lessons
  1. Which pairs of triangles are congruent?

    1. Congruence and congruent triangles

    2. Determining congruence by examining the angles in the triangle

    3. congruent triangles with equal sides and angles
  2. In the following diagram,  GHK\triangle\ GHK \cong  QRS\triangle\ QRS.
    Congruence and congruent triangles
    i) Find.
    1. m G\angle\ G = ?
    2. m R\angle\ R = ?
    3. SR = ?
    4. HK\overline{HK} = ?
    5. Find m R\angle\ R.
  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.
    Congruence and congruent polygons
  4. Write a two-column proof.

    1. Proof congruence and congruent triangles
      Given: AC\overline{AC}\congBD\overline{BD}, AD\overline{AD}\congBC\overline{BC},  CAD\angle\ CAD\cong CBD\angle\ CBD,  ADC\angle\ ADC\cong BCD\angle\ BCD
      Prove:  ACD\triangle\ ACD\cong BDC\triangle\ BDC
    2. Given: XC\overline{XC}\congZC\overline{ZC}
      CY\overline{CY} bisects XZ\overline{XZ}
      Prove:  XCY\triangle\ XCY\cong ZCY\triangle\ ZCY
      Proof congruence and congruent triangles in a two-column proof
  5. Write a flow proof
    1. Given: AC\overline{AC}\congBD\overline{BD}, AD\overline{AD}\congBC\overline{BC},  CAD\angle\ CAD\cong CBD\angle\ CBD,  ADC\angle\ ADC\cong BCD\angle\ BCD
      Prove:  ACD\triangle\ ACD\cong BDC\triangle\ BDC
      Proving the triangles are congruent in a flow proof
    2. Given: XC\overline{XC}\congZC\overline{ZC}
      CY\overline{CY} bisects XZ\overline{XZ}
      Prove:  XCY\triangle\ XCY\cong ZCY\triangle\ ZCY
      How to prove congruence and congruent triangles