What is a congruent angle?

In geometry, congruent angles are angles that have the same measure. This means that if two angles have the same degree or radian value, they are congruent. Congruency doesn't depend on the length of the sides of the angle, only on the angle's opening or measure.

Here are some key aspects of congruent angles:

• Definition: Two angles are congruent if and only if they have the same measure.

• Notation: The symbol for congruence is "≅". So, if angle A is congruent to angle B, we write ∠A ≅ ∠B.

• Properties: Congruence is an equivalence relation, meaning it is reflexive (∠A ≅ ∠A), symmetric (if ∠A ≅ ∠B, then ∠B ≅ ∠A), and transitive (if ∠A ≅ ∠B and ∠B ≅ ∠C, then ∠A ≅ ∠C).

• Examples:

  • Two right angles are always congruent, because they both measure 90 degrees.
  • Angles formed by the intersection of two parallel lines and a transversal line can often have congruent angles (e.g., <a href="https://www.wikiwhat.page/kavramlar/alternate%20interior%20angles">alternate interior angles</a> are congruent).

• Applications: Congruent angles are essential in proving the <a href="https://www.wikiwhat.page/kavramlar/congruence%20of%20triangles">congruence of triangles</a> and other geometric figures. For example, if two triangles have two pairs of congruent sides and the included angles are congruent (Side-Angle-Side congruence), then the triangles are congruent.