Congruent Angles
Congruent angles are angles that have the same measure
Congruent angles are angles that have the same measure. In other words, if two angles are congruent, it means they have the same number of degrees or radians. Congruent angles are denoted by the symbol ≅.
To determine if two angles are congruent, you can compare their measures using a protractor. If the measures of the two angles are equal, then they are congruent.
There are a few properties and theorems related to congruent angles:
1. Reflexive Property: Every angle is congruent to itself. For example, angle A is congruent to angle A.
2. Symmetric Property: If angle A is congruent to angle B, then angle B is congruent to angle A. In other words, if angle A ≅ angle B, then angle B ≅ angle A.
3. Transitive Property: If angle A is congruent to angle B, and angle B is congruent to angle C, then angle A is congruent to angle C. This property allows us to compare angles indirectly. For example, if angle A ≅ angle B and angle B ≅ angle C, then we can conclude that angle A ≅ angle C.
4. Angle Addition: If two angles are congruent, then adding or subtracting the same angle to both of them will result in two new congruent angles. For example, if angle A ≅ angle B, then angle A + X ≅ angle B + X, and angle A – Y ≅ angle B – Y, where X and Y are the same measures in degrees or radians.
These properties and theorems help us solve geometry problems, prove geometric relationships, and make deductions based on the congruency of angles.
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