Triangles
Correspondence of Vertices, Angles and Sides of Triangles
Let us consider ΔABC and ΔXYZ as shown below.
It can be seen that points A, B and C are the vertices of ΔABC, and points X, Y and Z are the vertices of ΔXYZ.
If vertex X is the pair of vertex A, then we can say that vertex X corresponds to vertex A and it is symbolised as ‘A → X’. Similarly, if vertex A corresponds to vertex X, then it is symbolised as ‘X →A’. Hence, vertices A and X correspond to each other and it is symbolised as ‘A ↔ X’, which is read as‘there is one to one correspondence between A and X’.
Similarly, the correspondences B ↔ Y and C ↔ Z can also be formed.
All of these correspondences can be represented together as ‘ABC ↔XYZ’.
In the same way,there may be other correspondences between the vertices of ΔABCand ΔXYZ. All the possible correspondences between ΔABCand ΔXYZ are listed below.
Correspondence between vertices |
Correspondence written together |
(1)A ↔ X, B ↔ Y, C ↔ Z |
ABC↔ XYZ |
(2)A ↔ X, B ↔ Z, C ↔ Y |
ABC↔ XZY |
… |
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