Congruence and congruent triangles

Congruence and congruent triangles

Lessons

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

    Congruence and congruent triangles

    b)

    Determining congruence by examining the angles in the triangle

    c)

    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.
    a)
    m G\angle\ G = ?

    b)
    m R\angle\ R = ?

    c)
    SR = ?

    d)
    HK\overline{HK} = ?

    e)
    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.
    a)

    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

    b)
    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
    a)
    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

    b)
    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