Congruent complements theorem
The Congruent Complements Theorem states that if two angles are complementary to the same angle or congruent angles, then they are congruent to each other
The Congruent Complements Theorem states that if two angles are complementary to the same angle or congruent angles, then they are congruent to each other.
In simpler terms, if two angles have the same complement (the angle that, when added to them, gives a right angle), or if two angles are both equal to another angle, then they are equal to each other.
To understand this theorem better, let’s consider an example:
Suppose we have two angles, angle A and angle B. We also have a third angle, angle C, that is complementary to both angle A and angle B. In other words, angle C, when added to either angle A or angle B, gives a right angle.
If we know that angle A and angle C are congruent, and angle B and angle C are congruent, then by the Congruent Complements Theorem, we can conclude that angle A and angle B are congruent as well.
This theorem is helpful in solving geometry problems involving right angles and complementary angles. It allows us to establish relationships between angles based on their complements and make deductions about their congruency.
In summary, the Congruent Complements Theorem states that if two angles have the same complement or are equal to the same angle, then they are congruent to each other.
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