Congruence

Two figures are congruent if some sequence of rigid motions carries one exactly onto the other.

Not just "looks the same"

The test is whether it can be moved onto the other, which is something you can actually do.

Several moves are allowed

A flip then a slide is fine. Any number of rigid motions, in any order.

What follows

Congruent figures have equal matching sides and equal matching angles, because rigid motions preserve both.

Congruent means reachable by rigid motions

Two figures are congruent if some sequence of translations, reflections and rotations carries one exactly onto the other. This is a stronger and more useful definition than "same shape and size", because it tells you how to check.

Corresponding parts are equal

If two figures are congruent, every matching pair of sides is equal and every matching pair of angles is equal. The word "corresponding" matters — you must identify which part maps to which before comparing anything.

The order of the letters carries information

Writing triangle ABC ≅ triangle DEF says A maps to D, B to E and C to F. The order is not decorative; it states the correspondence. A congruence written with the letters in the wrong order is a false statement.

Congruent is not the same as equal

Two distinct triangles can be congruent — they are different objects with identical measurements. "Equal" would mean they are the same triangle. The separate word exists because geometry cares about that distinction.