Similar PPT courseware 2 of the graphics "Parallel lines are proportional to their segments"

Description

Similar PPT courseware 2 of the graphics "Parallel lines are proportional to their segments"

learning target

1. Understand the process of producing the basic fact that the segments of parallel lines are proportional

2. Master the inference that the line segments divided by parallel lines are proportional

3. Be able to use the facts and inferences that parallel lines divide line segments into proportions to solve related calculation and proof problems

review review

1. The concept of proportional line segments:

Among the four line segments a, b, c, d, if a ∶ b = c ∶ d, then these four line segments a , b , c , d are called proportional line segments, or proportional line segments for short.

2. Basic properties of proportion

⑴.If a∶b＝c∶d, then a·d＝b·c.

⑵If a · d ＝b · c (a, b, c, d are not equal to 0), then a ∶b ＝c ∶d

Discuss:

1. How to understand "corresponding line segment"?

2. What are the expressions for the proportion of "corresponding line segments"?

"Correspondence" is a basic concept of mathematics.

Under the conditions l1∥l2∥l3, one of the following conclusions can be derived:

Applying this theorem to triangles yields its important corollary.

As shown in the figure, in △ABC, E and F are points on AB and AC respectively, and EF∥BC.

(1) If AE=7, EB=5, FC=4. Then what is the length of AF?

(2) If AB=10, AE=6, AF=5. Then what is the length of FC?

What did you learn in this lesson?

1. The proportional theorem of parallel line segments

When two straight lines are intercepted by a set of parallel lines, the resulting corresponding line segments are proportional

2. Inference

A straight line parallel to one side of a triangle intersects the other two sides, and the corresponding line segments intercepted are proportional.

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For more information about the PPT courseware "Similarities of Proportional Figures of Parallel Lines Divided into Line Segments", please click the Similar ppt tag of Proportional Figures of Parallel Lines Divided into Line Segments.

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Update Time: 2024-10-03

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