ME-Transformations and Congruence

A transformation is an operation that moves or changes a shape to create a new shape. The main types of transformations are translations, rotations, reflections, and dilations.

Congruent means that two shapes are identical in shape and size, meaning they can be superimposed on each other.

The SSS (Side-Side-Side) Congruence Postulate states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

The SAS (Side-Angle-Side) Congruence Postulate states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

The ASA (Angle-Side-Angle) Congruence Postulate states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.

The AAS (Angle-Angle-Side) Theorem states that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

The HL (Hypotenuse-Leg) Theorem states that if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

A rotation is a transformation that turns a shape around a fixed point, known as the center of rotation, by a certain angle.

To rotate a point (x, y) 180° about the origin, the new coordinates will be (-x, -y).

A reflection is a transformation that flips a shape over a line, creating a mirror image of the original shape.