Formulate and prove a theorem expressing the first criterion for the equality of triangles.

| November 17, 2020 | education

If two sides and the angle between them of one triangle are respectively equal to two sides and the angle between them of another triangle, then such triangles are equal to each other.
Evidence:
Let ABC and A1B1C1 be triangles for which AB = A1B1, AC = A1C1 and angle A = angle A1.
1. Set aside the angle В1А1С1 in the same half-plane with the AC boundary, where the angle BAC lies, so that the А1С1 side coincides with the AC side.
2. Since the angle BAC = angle B1A1C1, then according to the axiom of the deposition of the angle, the rays AB = A1B1.
3. Since AB = A1B1, then in the axiom of uniqueness of postponing the segment on the ray point B1 coincides with point B, point C1 coincides with point C. Therefore, BC coincides with B1C1. Then all the angles and sides of triangles ABC and A1B1C1 coincide. The theorem is proved.



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