Questions: Use the drop-down menus to explain if the two figures below are congruent, similar, or neither. If the figures are similar, state the scale factor.

Solution Steps

The coordinates of the vertices of _GHIJ_ are _G_(-10, 7), _H_(-8, 9), _I_(-6, 9), _J_(-4, 2) and _K_(-7, 2).

The lengths of the sides of _GHIJ_ are: _GH_ = $\sqrt{(-8 - -10)^2 + (9 - 7)^2}$ = $\sqrt{4 + 4}$ = $\sqrt{8}$ = $2\sqrt{2}$ _HI_ = $\sqrt{(-6 - -8)^2 + (9 - 9)^2}$ = $\sqrt{4 + 0}$ = 2 _IJ_ = $\sqrt{(-4 - -6)^2 + (2 - 9)^2}$ = $\sqrt{4 + 49}$ = $\sqrt{53}$ _JK_ = $\sqrt{(-7 - -4)^2 + (2 - 2)^2}$ = $\sqrt{9 + 0}$ = 3 _KG_ = $\sqrt{(-10 - -7)^2 + (7 - 2)^2}$ = $\sqrt{9 + 25}$ = $\sqrt{34}$

The coordinates of the vertices of _BCDEF_ are _B_(-7, -6), _C_(-6, -9), _D_(-4, -9), _E_(-2, -2), and _F_(-4, -2).

The lengths of the sides of _BCDEF_ are: _BC_ = $\sqrt{(-6 - -7)^2 + (-9 - -6)^2}$ = $\sqrt{1 + 9}$ = $\sqrt{10}$ _CD_ = $\sqrt{(-4 - -6)^2 + (-9 - -9)^2}$ = $\sqrt{4 + 0}$ = 2 _DE_ = $\sqrt{(-2 - -4)^2 + (-2 - -9)^2}$ = $\sqrt{4 + 49}$ = $\sqrt{53}$ _EF_ = $\sqrt{(-4 - -2)^2 + (-2 - -2)^2}$ = $\sqrt{4 + 0}$ = 2 _FB_ = $\sqrt{(-7 - -4)^2 + (-6 - -2)^2}$ = $\sqrt{9 + 16}$ = $\sqrt{25}$ = 5

The ratio of corresponding side lengths are not equal. For example, _HI_: _CD_ = 2 : 2 = 1, _IJ_: _DE_ = $\sqrt{53}$ : $\sqrt{53}$ = 1, but _JK_: _EF_ = 3 : 2. Since not all corresponding sides have the same ratio, the figures are not similar and therefore not congruent.

Final Answer: Neither