(1) Definition: If the sum of two angles is a right angle, the two angles are called complementary angles.
If the sum of two angles is a right angle, then these two angles are called complementary angles, and one angle is called complementary angles of the other angle.
(2) The nature of complementary angle and complementary angle
complementary angle
complementary angle
magnitude relation
∠ 1+∠2=90
∠ 1+∠2= 180
nature
Equiangular complementary angles are equal.
Equal complementary angles are equal.
(1) complementary angle and complementary angle refer to the quantitative relationship between two angles, and three or more angles with a sum of 90 (or 180) are not called complementary angles (or complementary angles);
(2) an angle with a degree equal to 90 (or 180) is a right angle (or right angle);
③ The complementary angles (or complementary angles) of equal angles are also equal;
(4) If the sum of two angles is equal to 180, and there is a public side and the other two sides are opposite extension lines, then these two angles are called adjacent complementary angles;
⑤ The complementary angle of ∠ α can be expressed as (90-∠α), and the complementary angle of ∠αcan be expressed as (180-∠α). Then the complementary angle of ∠ α-the complementary angle of ∠α =( 188)∠α is equal to the complementary angle of ∠αminus 90.
2. Definition and properties of vertex angle.
Definition of (1): As shown in the figure, ∠ 1 and ∠3, ∠2 and ∠4 have a common vertex, and the two sides of ∠ 1 are the opposite extension lines of ∠3 respectively.
(2) the nature of vertex angle
The vertex angles are equal.
As shown in the figure, ∠ 1 = ∠ 3, ∠ 2 = ∠ 4.
Understand the similarities and differences between vertex angle and adjacent complementary angle with graphics,
Similarities: ① There is a common vertex;
② Both of them are two angles with both positional and quantitative relations.
The differences are as follows: ① Diagonal corners have no common edges, and adjacent complementary corners have common edges;
② The quantitative relationship of vertex angles is equal, and the quantitative relationship of adjacent complementary angles is complementary.