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Geometry: Congruence

Problems

Proving Similarity of Triangles

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Problem : Is triangle ABC similar to triangle DEF? If so, by which method can you prove their congruence?

Yes, by AA

Problem : Is triangle ABC similar to triangle DEF? If so, by which method can you prove their congruence?

Yes, by SSS

Problem : Is triangle ABC similar to triangle DEF? If so, by which method can you prove their congruence?

No. Two pairs of corresponding sides are proportional, and one corresponding angle pair is congruent, but this angle is not the angle included in the proportional sides. Thus, there is not enough information to prove that the triangles are similar. It is a case of "SSA", which is not sufficient to prove similarity.

Problem : Is triangle ABC similar to triangle DEF? If so, by which method can you prove their congruence?

Yes, by AA

Problem : Is triangle ABC similar to triangle DEF? If so, by which method can you prove their congruence?

Yes, by SAS

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