If you know that corresponding angles in triangles GHI and JKL are congruent, do you know that the triangles are congruent? Explain, please. :)

Question

anonymous · Answer

Help?

sirm3d · Answer

no. triangle congruence requires that at least one pair of corresponding sides must be congruent for the two triangles to be congruent.
consider ALL equilateral triangles that you can draw. all the corresponding angles are congruent (each 60 degrees), yet you will find at two of the triangles drawn that are not congruent

anonymous · Answer

But I thought that only congruent triangles had corresponding angles?

kirbykirby · Answer

If they have the same angles, they may be of different size. |dw:1358729416932:dw|

kirbykirby · Answer

By a "homothetic transformation" (I'm not sure what other terminology is used... I learnt this terminology).

kirbykirby · Answer

|dw:1358729550548:dw| Maybe like this it's more obvious. Both triangles have the same angle, but they are not congruent (congruency requires that both triangles have the same length for its sides, and the same angles)