Congruent Angles: Definition, Examples, Chart, and Practice

What are congruent angles?

Congruent angles are angles that have the same measure.

They can be turned, moved, or drawn in different places. If the degree measure is the same, the angles are congruent.

The symbol for congruent is ≅, so ∠A ≅ ∠B means angle A is congruent to angle B.

Congruent angle rule

Use this rule when a diagram says two angles match.

If two angles are congruent, their measures are equal.

So if ∠A ≅ ∠B and ∠A is 58°, then ∠B is also 58°.

How diagrams mark congruent angles

Diagrams often use matching arc marks to show congruent angles.

One arc on each angle means those two angles match. Two arcs on each angle would mark a different matching pair.

When two lines cross, vertical angles are a common example of congruent angles.

Congruent angles in equations

Congruent angles let you set measures equal.

If one angle is labeled 3x + 8 and its congruent angle is 71°, write 3x + 8 = 71.

Then solve the equation to find the unknown value.

Worked example

Problem: ∠R and ∠S are congruent. ∠R measures 46°. What is the measure of ∠S?

Step 1: Congruent angles have equal measures.

Step 2: Since ∠R = 46°, ∠S must also be 46°.

Answer: ∠S measures 46°.

Congruent angles and proofs

In later proof lessons, congruent angle marks are used as evidence.

For example, Angle-Angle-Side uses matching angles and a matching side to prove triangles congruent.

The idea is the same: matching marks tell you which parts have equal measures.

Common mistakes

Do not say angles are congruent just because they look close in size. Use given measures, matching marks, or a rule.

Do not confuse congruent angles with adjacent angles. Adjacent angles sit next to each other, but they are not always equal.

Do not change the measure because an angle is turned sideways. Rotation does not change angle size.

Quick practice

1. If ∠A ≅ ∠B and ∠A = 72°, then ∠B = 72°.

2. Two angles marked with the same arc mark are congruent unless the diagram says otherwise.

3. Angles can be congruent even when they face different directions.

4. If ∠M ≅ ∠N and ∠N = 5x, then ∠M can be set equal to 5x.