Geometry for elementary academy The Side-Angle-Side accordance assumption

 05 July 12:14   

    In this chapter, we will altercate addition accordance theorem, this time the Side-Angle-Side theorem.

    The assumption appears as Based on [http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI4.html Book I, prop 4]

    at the Elements.

    Given two triangles $riangle\; ABC$ and $riangle\; DEF$ such that their abandon are equal, hence:

    # The ancillary $overline$ equals $overline$.

    # The ancillary $overline$ equals $overline$.

    # The bend $angle\; CAB$ equals $angle\; FDE$ (These are the angles amid the sides).

    Then the triangles coinciding and their additional angles and ancillary are according too.

    We will use the adjustment of superposition – we will move one triangle to the additional one and we will appearance that they coincide.

    We won’t use the architecture we abstruse to archetype a band or a articulation but we will move the triangle as whole.

    # Superpose $riangle\; ABC$ on $riangle\; DEF$ such that A is abode on D and $overline$ is placed on $overline$.

    # It is accustomed that $overline$ equals $overline$.

    #Hence, B coincides with E.

    # It is accustomed that the bend $angle\; CAB$ equals $angle\; FDE$.

    # Hence, $overline$ is placed on $overline$.

    # it is accustomed that $overline$ equals $overline$.

    #Hence, C coincides with F.

    # Therefore, $overline$ coincides with $overline$.

    # The triangles $riangle\; ABC$ and $riangle\; DEF$ coincide.

    # The triangles $riangle\; ABC$ and $riangle\; DEF$ congruent.