Congruent Angles

Congruent angles are two or more angles with equal measures in degrees as well as in radians. The direction or length of the lines does not make any difference on congruency.

We know that all angles in an equilateral measure the same; that is 60°.

So, the angles in an equilateral triangle are congruent angles.

Example: If line CD bisects another line AB at the point O, then which of the following is true?

A) ∠AOB ≅ ∠AOD

B) ∠COB ≅ ∠BOD

C) ∠AOD ≅ ∠COB

D) ∠COD ≅ ∠AOC

∠AOD ≅ ∠COB as these are vertically opposite angles and hence their measure is the same.

Check Point

Which are the congruent angles in the given triangles?

2. What is the value of x if the given two angles are congruent?

3.Find the value of b.

4.What is the value of x, if in the given triangles, ∠ABC ≅ ∠RPQ?

5.Do congruent angles measure the same in degrees and radians?

Answer key

∠ACB ≅ ∠PRQ
34
40°
47°
Yes

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