"Review" Intersecting lines and parallel lines PPT courseware

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"Review" Intersecting lines and parallel lines PPT courseware

1. Supplementary angles: Among the four angles formed by the intersection of two straight lines, the two angles that have a common vertex and a common side are supplementary angles.

2. Opposite angles: (1) Among the four angles formed by the intersection of two straight lines, the two angles that have a common vertex but no common sides are opposite angles.

(2) The two sides of one angle are the reverse extension lines of the two sides of the other angle. These two angles are opposite vertex angles.

3. Properties of adjacent supplementary angles: Supplementary angles of the same angle are equal.

4. Properties of opposite vertex angles: opposite vertex angles are equal.

Two characteristics: (1) have common vertices;

(2) The two sides of the angle are opposite extensions of each other.

5. If n straight lines intersect at one point, there will be n (n-1) pairs of opposite vertex angles.

intersect

1. Lines AB and CD intersect at O. How many pairs of pairs of vertex angles are there in the figure? Adjacent supplementary angle?

When one angle is determined, are the sizes of the other three angles determined?

2. Lines AB, CD, and EF intersect at O. How many pairs of vertex angles are there in the figure?

∠The subtended vertex angle of AOC is _______

∠The opposite vertex angle of COF is _______

∠The supplementary angle of AOC is _______

∠The supplementary angle of EOD is _______

1. Definition of perpendicular line: When two straight lines intersect and one of the four angles formed is 90°, the two straight lines are said to be perpendicular to each other. One of the straight lines is called the perpendicular to the other straight line. Their intersection is called the vertical foot.

2. Properties of perpendicular lines: (1) There is and is only one straight line perpendicular to the known straight line passing through a point.

Property (2): Among all the line segments connecting a point outside the straight line and each point on the straight line, the perpendicular segment is the shortest. Abbreviation: The vertical segment is the shortest.

3. Distance from point to straight line: The length of the perpendicular segment from a point outside the straight line to the straight line is called the distance from point to straight line.

4. When encountering line segments and line segments, line segments and rays, rays and rays, line segments or rays perpendicular to straight lines, it especially means that the straight lines where they are located are perpendicular to each other.

5. A vertical line is a straight line, and a vertical line segment specifically refers to a line segment as a figure. The distance from a point to a straight line refers to the length of the vertical line segment, which refers to a quantity and has a unit.

1. The concept of parallel lines: Two straight lines that do not intersect in the same plane are called parallel lines.

2. The positional relationship between two straight lines: In the same plane, there are only two positional relationships between two straight lines: (1) intersecting; (2) parallel.

3. Basic properties of parallel lines: (1) Parallel axiom (the existence and uniqueness of parallel lines) passing through a point outside the straight line, there is and is only one straight line parallel to the known straight line.

(2) Corollary (transitivity of parallel lines) If two straight lines are parallel to a third straight line, then the two straight lines are also parallel to each other.

4. Concepts of congruent angles, interior angles, and congruent interior angles

Concentric angles, internal angles, and internal angles on the same side refer to the special positional relationship between angles that do not share a vertex among the eight angles formed by the intersection of a straight line and two straight lines respectively.

Like opposite vertex angles and adjacent supplementary angles, they always exist in pairs.

practice

(1) ∠1 and ∠9 are angles ____ cut by straight lines ____ and ____ by straight lines ____;

(2) ∠6 and ∠12 are angles ____ cut by straight lines ____ and ____ by straight lines ____;

(3) ∠4 and ∠6 are angles ____ cut by straight lines ____ and ____ by straight lines ____;

(4) The co-position angle formed by straight lines AB and CD cut by straight line EF____ is ____;

1. The concept of proposition: A sentence that judges one thing is called a proposition.

A proposition must be a complete sentence; the sentence must make a positive or negative judgment about something. Both are indispensable.

2. The composition of propositions: Each proposition consists of two parts: proposition and conclusion.

The proposition is the known matter; the conclusion is the matter deduced from the known matter. Propositions are often written as

"If..., then..." form. Or "If..., then..." and other forms.

3. True propositions and false propositions: A proposition is a judgment, which may be correct or wrong. From this, propositions can be divided into true propositions and false propositions.

A true proposition is a proposition that if the proposition is true, then the conclusion must be true.

A false proposition is a proposition that cannot guarantee that the conclusion will always be true if the proposition is true.

Example 1. Determine whether the following statement is a proposition. If it is a proposition, is it a true proposition or a false proposition?

(1) Draw line segment AB=2cm

(2) Right angles are all equal;

(3) How many intersection points are there when two straight lines intersect?

(4) If two angles are not equal, then the two angles are not opposite vertex angles.

(5)Equal angles are right angles;

Analysis: Because (1) and (3) are not sentences that judge a certain thing, (1) and (3) are not propositions.

Solution. (1) and (3) are not propositions; (2), (4) and (5) are propositions; (2) and (4) are both true propositions, and (5) is a false proposition.

1. Definition of translation transformation: If you move a graphic as a whole in a certain direction, a new graphic will be obtained. Such graphic movement is called translation transformation, or translation for short.

Properties of translation: (1) Translation does not change the shape and size of the graph.

(2) Line segments connected by corresponding points are parallel (or collinear) and equal.

The factors that determine translation are the direction and distance of translation.

After translation, every point on the graph moves the same distance in the same direction.

After translation, the corresponding angles are equal; the corresponding line segments are parallel (or collinear) and equal;

Line segments connecting corresponding points are parallel (or collinear) and equal.

Operation and explanation:

There is such a question in the mathematics class: "As shown in the figure, with point B as the vertex and ray BC as one side, use a ruler and compass to calculate ∠EBC so that ∠EBC=∠A. Are EB and AD necessarily parallel?" Xiao Wang said "it must be parallel"; while Xiao Li said "it is not necessarily parallel". Whose view do you agree with more?

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"Intersecting Lines" Intersecting Lines and Parallel Lines PPT Courseware 3:

"Intersecting Lines" Intersecting Lines and Parallel Lines PPT Courseware 3 Knowledge Points Adjacent Supplementary Angle If two angles have a common side and their other sides are reverse extensions of each other, then the two angles are adjacent supplementary angles. In the figure, the angles that are complementary to each other are: 1 and 2, 2 and 3, 3 and 4, and 1 and 4. ..

"Review" Intersecting Lines and Parallel Lines PPT Courseware 3:

"Review" Intersecting Lines and Parallel Lines PPT Courseware 3 1. Learning Objectives 1. Further consolidate the concepts and properties of adjacent supplementary angles and subtended angles 2. Understand the concepts and properties of perpendicular lines and perpendicular line segments 3. Master the meaning of two parallel lines Determination and properties 4. Understand graphics through translation..

"Review" Intersecting Lines and Parallel Lines PPT Courseware 2:

"Review" Intersecting Lines and Parallel Lines PPT Courseware 2 Question What is the difference between mutually adjacent and supplementary angles? Supplementary angles - they have a common side and their other sides are opposite extensions of each other; their sum is 180. Supplementary angles---their positions are uncertain..

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Update Time: 2024-10-16

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