Congruent Angles

In geometry, 2 figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

Definitions of Congruent Angles

Angles are congruent if they have the same angle measure in degrees. They can be at any orientation on the plane.

In case of angles, “congruent” is similar to saying “equals”. You could say “the measure of angle A is equal to the measure of angle B”. But in geometry, the correct way to say it is “angles A and B are congruent”.

Congruent Angles are 2 (or more) angles that have the same angle (in degrees or radians).

To be congruent, the angles measure must be the same, the length of the two arms making up the angle is irrelevant.

Examples

These angles are congruent.

 Congruent Angles 30 Degree 1       Congruent Angles 30 Degree 2       Congruent Angles 30 Degree 3     These 3 angles are congruent because they have 30o (same angle)
  Congruent Angles 60 Degree 1             Congruent Angles 60 Degree 2   Congruent Angles 60 Degree 3These 3 angles are congruent because they have 60o (same angle)
      Congruent Angles 90 Degree 1      Congruent Angles 90 Degree 2  Congruent Angles 90 Degree 3These 3 angles are congruent because they have 90o (same angle)

  • They don’t have to point in the same direction.
  • They don’t have to be on similar sized lines.
  • Just the same angle.

Remember!!

The length of the angles’ edges or the direction of the angles has no effect on their congruency.

As long as their measure is equal, the angles are considered congruent.

Symbols of Congruence

The symbol for congruence is

Also recall that the symbol for an angle is , so the statement

∠ABC ≅ ∠DEF

is read as “The angle ABC is congruent to the angle DEF”.

Learn More

Complementary Angles

How To Find if Triangles are Congruent

Adjacent Angles

Alternate Exterior Angles

Geometry Index

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