What are the proofs of triangle congruence theorems?

What are the proofs of triangle congruence theorems?

Triangle congruence theorems include SSS, SAS, ASA, AAS, and HL. Would you like to know the proof for a specific one?

Can you explain the proof for the SSS theorem?

Sure! The SSS (Side-Side-Side) theorem states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent. The proof involves showing that the triangles can be superimposed on each other.

What about the SAS theorem?

The SAS (Side-Angle-Side) theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent. The proof typically uses the properties of isosceles triangles and congruence.

Can you give me an example of how to use the ASA theorem?

Absolutely! The ASA (Angle-Side-Angle) theorem states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent. For example, if you have triangle ABC and triangle DEF where angle A = angle D, angle B = angle E, and side AB = side DE, then triangle ABC is congruent to triangle DEF.