Congruent Angles: Definition, Symbol and Key Theorems

Are these angles congruent? By the end of this article, you'll be able to answer that question. dddb / Getty Images

Two congruent angles are simply pairs of angles with equal measures. You can find congruent angles examples in hundreds of everyday objects.

For instance, think of any time you've tried to draw a simple sketch of a house. You'll like draw a perfect square or rectangle by drawing congruent angles to form the box, and then congruent triangles (equilateral triangles) form the pitched roof.

Identifying Congruent Angles

An easy way to remember congruent angles is to relate the word "congruent" and to how that term is used in reference to parallel lines: Two parallel lines with the same measure are congruent. The same principle works for interior angles.

If two angles equal the same angle measure, then they are congruent. Two or more angles may be called congruent angles as well (not just a pair).

What Is the Congruent Angles Symbol?

The symbol that represents corresponding angles being congruent in two figures is "≅."

To illustrate this, use the example of two triangles, one called Triangle ABC and the other Triangle PQR. If the triangles are congruent and each geometric figure has interior angles of equal measure, you can write the following pairs:

Angle ABC ≅ Angle PQR

Angle CAB ≅ Angle RPQ

5 Congruent Angle Theorems

In geometry, the following congruent angles theorems dictates the different rules given angles must abide by to prove that the corresponding angles are congruent.

1. Vertical Angles Theorem

This theorem dictates that vertically orientated, alternate interior angles of two rays intersecting will always be equal. This is because each of the two lines creates a line segment where both angles on the same side must equal 180 degrees, with the other angle mirroring the opposite side.

2. Corresponding Angles Theorem

This example occurs when two parallel lines are intersected by a third straight line. With both parallel lines cut, the adjacent angles and corresponding sides will share the same shape created by the line segment.

3. Alternate Angles Theorem

This theorem builds on the same principles as the concept of the corresponding angle, except that the bisecting ray will construct congruent angles on opposite corners of the transversal line.

4. Congruent Supplements Theorem

This theorem dictates that the supplementary angles of linear pairs are interchangeable between congruent figures. Not all congruent angles add up to 180 degrees, though, so this rule only works when two angles are congruent along a straight line.

5. Congruent Complements Theorem

Constructing congruent angles is easiest when an angle bisector creates two pairs of equal angle measures on right-angle shapes with the same relative position.

This angle bisector between two arms at 90 degrees (right angle) makes it easier to see how the inverse angles are complementary instead of complex-angled shapes like isosceles triangles.