I. Definition of Complementary Angle
If the sum of two angles satisfies 180+2kπ (k ∈ z), then the two angles are complementary. One angle is called the complementary angle of another.
Note: The position of two corners does not affect their complementary angles. To judge whether the two angles are complementary, it is only necessary to satisfy that the sum of the two angles is equal to 180+360 k, k ∈ z.
Two. Properties of complementary angle
The same angle or the complementary angle of the same angle is equal.
It includes the following two aspects:
1. The complementary angles of the same angle are equal. That is, if ∠ A+∠C=∠B = 180, ∠ A+∠ C = 180, ∠C=∠B.
2. The complementary angles of equal angles are equal. Namely: ∠ A+∠C=∠B = 180, ∠ D+∠ C = 180, ∠A=∠D, then ∠ C =
Three. Adjacent complementary angle
1. Definition
These two corners have a common edge, and their other side is an extension line opposite to each other. The two angles with this relationship complement each other. The complementary angle only pays attention to the quantity relationship, and the sum of the two angles is 180, that is, whether there is a common edge, but the adjacent complementary angles should also pay attention to the position relationship).
2. Nature
The sum of an angle and its adjacent complementary angles is equal to 180.
If two angles are complementary, their bisectors are perpendicular to each other.
3. Characteristics
1. There is an ordinary vertex * * *;
2. Have a male relationship;
3. The other side of the two corners is the opposite extension line.
4. Adjacent complementary angles appear in pairs, which are mutually adjacent complementary angles.
5. Two adjacent corners make a right angle.
6. Two adjacent complementary angles are complementary, that is, the sum is 180 degrees.