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Geometry: Congruence

Problems

Proving Congruence of Triangles

More Ways to Prove Congruence

Problem : Can you prove triangle ABC congruent to triangle DEF? If so, by which method can you show that they are congruent?

No, sides AB and AC, whose lengths are four, correspond to sides DE and DF, whose lengths are 3.

Problem : Can you prove triangle ABC congruent to triangle DEF? If so, by which method can you show that they are congruent?

Yes, by SSS.

Problem : Can you prove triangle ABC congruent to triangle DEF? If so, by which method can you show that they are congruent?

No, two pairs of corresponding sides are congruent, and one pair of corresponding angles is congruent, but the angle is not included in the sides, so the situation doesn't fit into SSS, SAS, or ASA. It is more like "SSA", which is not sufficient to prove the congruence of triangles.

Problem : Can you prove triangle ABC congruent to triangle DEF? If so, by which method can you show that they are congruent?

No, each triangle is equiangular, and therefore equilateral, but the sides of one triangle could be longer or shorter than the sides of the other. Just because both triangles are equilateral doesn't mean that they must be congruent.

Problem : Is triangle ABC congruent to triangle DEF? If so, by which method can you show that they are congruent?

No, triangle ABC is congruent to triangle FDE, though. The vertices of triangles ABC and DEF don't correctly correspond for them to be congruent.

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