Question

Which are the properties of congruent triangles?

Answer 1

When two triangles are congruent they will have exactly the same three sides and exactly the same three angles. The equal sides and angles may not be in the same position (if there is a turn or a flip), but they are there.

Triangles are congruent if:

SSS (side side side) All three corresponding sides are equal in length. ...

SAS (side angle side) A pair of corresponding sides and the included angle are equal. ...

ASA (angle side angle) ...

AAS (angle angle side) ...

HL (hypotenuse leg of a right triangle)

Explained below

Any triangle is defined by six measures (three sides, three angles). But you don't need to know all of them to show that two triangles are congruent. Various groups of three will do. Triangles are congruent if:
SSS (side side side)
All three corresponding sides are equal in length.
See Triangle Congruence (side side side).
SAS (side angle side)
A pair of corresponding sides and the included angle are equal.
See Triangle Congruence (side angle side).
ASA (angle side angle)
A pair of corresponding angles and the included side are equal.
See Triangle Congruence (angle side angle).
AAS (angle angle side)
A pair of corresponding angles and a non-included side are equal.
See Triangle Congruence (angle angle side).
HL (hypotenuse leg of a right triangle)
Two right triangles are congruent if the hypotenuse and one leg are equal.
See Triangle Congruence (hypotenuse leg).