Proving triangles are congruent triangles uses theorems (postulates), the Angle Side Angle (ASA), Side Angle Side (SAS), Side Side Side (SSS), and AAS (Angle-Angle-Side). Two triangles with equal corresponding angles may not be congruent to each other because one triangle might be an enlarged copy of the other.
Triangles that have exactly the same size and shape are called congruent triangles. The congruent triangles can be used using the Angle Side Angle (ASA), Side Angle Side (SAS), Side Side Side (SSS), and AAS (Angle-Angle-Side) theorems.
Angle Side Angle (ASA) theorem states that if any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent.
Side-angle-side (SAS) 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, the triangles are congruent.
Side Side Side (SSS) theorem states that if all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent.
AAS (Angle-Angle-Side) theorem states that if two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.
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