Think about the order of the vertices in the statement.
Error: The order of the vertices in the triangle names is incorrect. Example Correction: △ JKL ≅ △ FGH by the ASA Congruence Theorem
Practice makes perfect
Looking at the given triangles and the congruence statement, we can see that the correct theorem was used. Angle-Side-Angle makes sense to show congruence of the two triangles because we are shown a congruent line between two congruent angles. Now, let's consider the given names of the triangles.
△ JKL ? ≅ △ FHG
The following diagram illustrates the order of the vertices as they have been named in the statement. You can follow the naming using the arrows or the color-scheme, blue- green- red.
The order of the vertices in the names are all incorrect! When naming congruent triangles, the congruent angles should be in the same order on both sides of the congruence statement. Here, we know the following to be true based on the markings shown in the diagram.
Angle:& ∠ J ≅ ∠ F
Side:& JK≅FG
Angle:& ∠ K ≅ ∠ G
These relationships mean that a correct name for the congruent triangle must include either JK and FG or KJ and GH in the same positions of the name. The following table includes all the possibilities of correct names.
Left-hand Triangle Name
≅
Right-hand Triangle Name
△ JKL
≅
△ FGH
△ JLK
≅
△ FHG
△ KJL
≅
△ GFH
△ KLJ
≅
△ GHF
△ LKJ
≅
△ HGF
△ LJK
≅
△ HFG
Therefore, a possible corrected statement could be:
△ JKL ≅ △ FGH
by the ASA Congruence Theorem.
