Explain Triangle Congruency Rules

Question

Explain why different combinations of equal angles and sides are or are not accepted as proving that triangles are congruent.

Answer 1

SAS

ASA

SSS

AAS

all prove that 2 triangles are congruent.

The first 3 can be proved without the parallel postulate; the 4th one requires the parallel postulate.

Draw a figure when 2 sides and an angle are equal...when the angle is a right angle the triangles are congruent but not otherwise.

Answer 2