Define Congruent Angles

Congruent Angles (compass)

Before you study this topic; you are adviced to read: 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