Analyze the length of the sides that meet at each vertex.
Jasmine and Will are both correct, see solution.
Practice makes perfect
We can identify the corresponding vertices by checking the lengths of the sides that meet at that particular vertex. We will use different colors for the different corresponding vertex pairs.
A valid congruence statement lists corresponding vertices in the same order. Let's check both statements.
Person
Congruence Statement
Is the order correct?
Is the statement valid?
Jasmine
△ C A B≅△ Z Y X
Yes
Yes
Will
△ A B C≅△ Y X Z
Yes
Yes
We can see that Jasmine and Will are both correct.
Extra
Writing a Congruence Statement
As with polygons, when it comes to writing a triangle congruence statement, the order in which the vertices are written is critical. Naming them in an incorrect order leads to erroneous conclusions. Consider, for example, the following congruent triangles.
Although the triangles are congruent, the congruence statement △ ABC ≅ △ MQT is incorrect. Why? Because it would lead to the following conclusions about the sides and angles.
Consequently, always be sure to list the corresponding vertices in the correct order. Furthermore, another important concept to consider is that the claim which helps to determine whether two triangles are congruent is also valid for polygons. In fact, the claim is identical, except that triangles has been replaced by polygons.
