Suppose I have the figure in the image marked 'Original':
Visually, that figure appears to be a parallelogram.
Would the following proof that $\bigtriangleup BCA \cong \bigtriangleup DAC$ be valid?
- $BC \parallel AD$, because Diagram
- $\angle BAC \cong \angle DCA$, because Alternate Interior Angles
- $AC \cong AC$, because Reflexive Property of Congruence
- $AB \cong CD$, because Diagram
- $\bigtriangleup BCA \cong \bigtriangleup DAC$, because Side-Angle-Side congruence postulate
I ask because the figure marked 'Alternate' has the same markings ($AB \cong CD$, $BC \parallel AD$), but side CD is in a different position and side AD is longer, so the two triangles are not congruent. So I'm not sure whether you can say that the original figure is in fact a parallelogram, just based on the information shown, which must be true for step 2 in the proof to be valid.