Suppose ΔHEN is congruent to ΔBIG. List all the other correct ways of expressing this congruence.
All correct ways to express the congruence are:
ΔHEN ≅ ΔBIG ΔNEH ≅ ΔGIB ΔENH ≅ ΔIGB ΔHNE ≅ ΔBGI ΔEHN ≅ ΔIBG ΔNHE ≅ ΔGBI
These are the 6 possible ways to write the congruence by maintaining the correspondence H↔B, E↔I, N↔G.
Explanation
The chapter explains that when writing congruence, the order of vertices matters. The first vertex of ΔHEN corresponds to the first vertex of ΔBIG, and so on. Since H corresponds to B, E corresponds to I, and N corresponds to G, we must maintain this correspondence in all expressions. The 6 permutations that maintain the correct correspondence are valid.
Solution Steps
The order of vertices in congruence statements matters - corresponding vertices must be in the same position
From ΔHEN ≅ ΔBIG, identify the correspondence: H↔B, E↔I, N↔G
Generate all 6 permutations of (H, E, N) and apply the same permutation to (B, I, G)
List all valid congruence statements that maintain the correspondence