How many corresponding sides have to be congruent in two triangles for the triangles themselves to be congruent?
The statement is not true. Explanation: See solution.
Practice makes perfect
From the diagram, there are a couple of things we notice. First, the two triangles share a side, AC. Therefore, by the Reflexive Property of Congruence, we know this side is congruent in the two triangles. Additionally, BC and AD are equal in length and are congruent as well. Let's mark this in our diagram.
To be able to claim congruence, all corresponding sides have to be congruent. However, from the diagram we see that this is not the case as AB and DC have different lengths. Therefore, the triangles cannot be congruent and the statement is not true.
