"Supplementary Angle and Supplementary Angle" Parallel Lines and Intersecting Lines PPT Courseware 4

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"Supplementary Angle and Supplementary Angle" Parallel Lines and Intersecting Lines PPT Courseware 4

supplementary angles

Generally speaking, if the sum of two angles is equal to 90° (right angle), the two angles are said to be supplementary angles. That is, each angle is the supplementary angle of another angle.

Please judge:

(1)∠1+∠2=90°, then ∠1 is a supplementary angle. ( )

(2) ∠1 +∠2+ ∠3=90°, then ∠1, ∠2, ∠3 are supplementary angles to each other. ( )

The geometric language is expressed as:

If ∠1+∠2=90°, then ∠1 and ∠2 are complementary angles to each other

(∠1 is the supplementary angle of ∠2/∠2 is the supplementary angle of ∠1)

complementary angles

Generally speaking, if the sum of two angles is equal to 180° (straight angle), the two angles are said to be supplementary angles. That is, one of them is the supplementary angle of the other angle.

The geometric language is expressed as:

If ∠1+∠2=180°, then ∠1 and ∠2 are supplementary angles of each other (∠1 is the supplementary angle of ∠2/∠2 is the supplementary angle of ∠1)

The opposite is also true: if ∠1 and ∠2 are complementary angles, then ∠1+∠2=180°

practice

True or False:

1. If an angle has a supplementary angle, then the angle must be an obtuse angle ( )

Acute angles, right angles, and obtuse angles all have supplementary angles;

2. Two complementary angles cannot be equal. ( )

Two equal angles that are complementary are right angles;

3. An obtuse angle has no supplementary angle, but it must have a supplementary angle ( )

Expand applications:

1. An angle is three times its supplementary angle. What is the degree of this angle?

2. An angle is 20° smaller than its supplementary angle. What is its supplementary angle? 1. one

induction

Properties of supplementary angles: Supplementary angles of identical angles (congruent angles) are equal.

Properties of supplementary angles: Supplementary angles of identical angles (congruent angles) are equal.

Decide whether the following statements are correct

(1) The sum of 30, 70 and 80 is a straight angle, so these three angles are supplementary to each other. ( )

(2) The supplementary angle of an angle must be an acute angle. ( )

(3) The supplementary angle of an angle must be an obtuse angle. ( )

(4) The angle of 90 is a supplementary angle. ( )

(5) Whether two angles are complementary is related to both their size and their position. ( )

Summary

The concepts of supplementary angles and supplementary angles:

(1) Two angles whose sum is 90° are supplementary angles to each other;

(2) Two angles whose sum is 180° are supplementary angles;

Properties of supplementary angles and supplementary angles:

(1) The supplementary angles of same angles (congruent angles) are equal;

(2) The supplementary angles of identical angles (congruent angles) are equal;

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Update Time: 2024-07-09

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