Proving Triangles are Congruent

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To prove two triangles are congruent, it is sufficient two any of the following:

The lengths of corresponding sides of each triangle are the same. If triangle 1 has lengths 4, 5 and 6 cm, and triangle 2 has lengths of 4, 5 and 6 cm, then the triangles are congruent.

Each triangle has two corresponding equal angles and one corresponding equal side. If triangle 1 has angles 40 and 70 degrees, and a side of length 7 cm, and triangle 2 has corresponding angles 40 and 70 degrees and a corresponding side of length 7 cm then the triangles are congruent.

It is important that sides and angles correspond properly. The triangles below are not congruent because the sides do not correspond.

Each triangle has one corresponding angle and two corresponding sides. If triangle 1 has sides 6 and 7 cm and an angle 80 degrees and triangle 2 has corresponding sides 6 and 7 cm and a corresponding angle 80 of degrees, then the triangles are congruent


Proving triangles are congruent can involving inpspecting the diagram to find symmetries. If the triangles share a side, then automatically the have one length equal. The triangle below with a common side AB are congruent because they have a length in common, another corresponding length and two corresponding angles – the right angles at B.

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