Argument 1 Yes, the two shapes must be similar. If you draw segments $AC$ and $EG$, then you have two pairs of similar triangles. $\angle A \approx \angle E$ and $\angle D \approx \angle H$ so $\Delta ACD \sim \Delta EGH.$ Similarly $\Delta ACB \sim \Delta EGF.$ Because their two constituent triangles are similar, we must have $ABCD \sim EFGH.$ | Argument 2 No, it is possible the shapes are not similar. Consider the example above of two rectangles. All their angles are congruent, but the shapes are clearly not similar. |

*Who do you believe?*