Figures that have the same shape and size and can be superimposed exactly on each other.

By taking specific measurements, including lengths and angles, to ensure an exact replica.

Two triangles are congruent if all three sides in one triangle are equal to the corresponding sides in the other.

If two sides and the included angle of one triangle are equal to those of another triangle, the triangles are congruent.

If two angles and the included side in one triangle are equal to those in another, the triangles are congruent.

Using symbols, such as ΔABC ≅ ΔXYZ, indicating corresponding vertices and sides.

The angles opposite the equal sides are also equal.

If two angles in one triangle match two angles in another (AAS condition), the triangles are congruent.

If the hypotenuse and one other side is equal to the corresponding parts of another right triangle (RHS condition).

The triangles may not be congruent (SSA condition).

Two circles are congruent if their radii are equal.

Yes, all angles in an equilateral triangle are 60°, and all sides are equal.

They may differ in size; triangles can have the same shape but vary in scale.

All corresponding vertices, sides, and angles must be equal.

Using methods like tracing, measuring sides, or superimposing figures.

If two triangles share a common side and have equal lengths for the other sides, they are congruent.

Vertical angles are equal; they can help establish congruence in intersecting triangles.

Architectural structures like bridges often utilize congruent triangles for stability.

ΔACB ≅ ΔXZY is valid if the sides and angles correspond correctly.