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.

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