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Home >> Angles >> Congruent Angles >>

## Define Congruent Angles

 Congruent Angles (compass)

Define Congruent / Congruence
Define Rays and Line
Define Angles

When two angles have equal or same measure, they are said to be Congruent.

The reverse of the above statement also holds true:
"When two angles are congruent, they have equal or same measures".

Example 1: Below are two angles: ∠ ABC and ∠ PQR:

∠ ABC is as follows:

∠ PQR is as follows:

Now let's place both angles over each another and observe what happens:

We can see that both the angles coincide over each other exactly.
Note - To check congruency of two angles, we only check the measures of angles; not the length of their arms. Arms of the angle indicate the direction only.

Hence, we can say line segment ∠ ABC and ∠ PQR are congruent

Or we can also write it as

∠ ABC ≅ ∠ PQR:

Example 2: Below are two angles: ∠ XYZ and ∠ RST:

∠ XYZ is as follows:

∠ RST is as follows:

Now let's place both angles over each another and observe what happens:

We can see that both the ∠ XYZ and ∠ RST does not coincide over each other, as arms YX of ∠ XYZ and arm SR of ∠ RST are in different direction, thereby by forming ∠ XYZ and ∠ RST of different measures.
Hence, we can say line segment ∠ XYZ and ∠ RST are not congruent

Or we can also write it as

∠ XYZ ≇ ∠ RST