Congruence and congruent triangles

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