Two angles are congruent when their angle measurement is exactly the same.
Given above are two angles ∠BAC & ∠ DEF.
Note that both angles measure 70.4 degree, hence they are congruent angles.
∠BAC = ∠ DEF = 70.4 degree.
Note:
The congruent angles;
⟹ do not need to point at same direction.
⟹ the length of arm of angle can be different.
Symbol for Congruent Angles
In geometry, congruency between angles is shown by symbol \mathtt{\cong } .
Hence, if angles ∠BAC & ∠ DEF are congruent to each other, we can write;
∠BAC \mathtt{\cong } ∠ DEF
You need to remember the symbols as you have to use in widely in your geometry exams.
Congruent angles in different shape
Sometimes you need to find the congruency of angles present inside the given shape.
We know that shapes like triangle, rectangle, quadrilateral etc. are made of different angles. You may ask to check the congruency of angles present in these shapes.
For Example;
Consider the two triangles.
In the given triangles ABC and DEF, check if ∠A and ∠D are congruent or not.
Observe ∠A & ∠D inside the given triangles, you will note that both measure 55 degrees.
∠A = ∠D = 55 degree.
Since both angles are equal measure, they are congruent to each other.
∠A \mathtt{\cong } ∠D