Question

If the parts of two triangles are matched so that two angles of one triangle are congruent to the corresponding angles of the other, and so that a side of one triangle is congruent to the corresponding side of the other, then the triangles must be congruent. Justify this angleangle-corresponding side (AAS) criterion for congruence. Would AAS be a valid test for congruence if the word corresponding were left out of the definition? Explain.

Answer 1

if the two trangles are congruent ,then their correponding parts will be equal.

If two angle in one triangle are congruent to two angles of a second triangle, and one side is congruent, then the triangles are congruent. by AAS criterion

If in triangles ABC and DEF, angle A = angle D, angle B = angle E, and AC = DF, then triangle ABC is congruent to triangle DEF BY AAS

correponding is very important term here,

saying triangle ABC is congruent to triangle DEF is not the same as saying triangle ABC is congruent to triangle EFD.(although vertex is same)

because first statement means,that AC= DF and angle A = angle D,angle B = angle E. The second statement says that AC = DE and angle A = angle E. This is VERY DIFFERENT.