"Parallel lines are proportional to their segments" PPT courseware

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"Parallel lines are proportional to their segments" PPT courseware

1. When two straight lines are intercepted by a set of parallel lines, the corresponding line segments intercepted are _________.

2. If a straight line parallel to one side of a triangle cuts the other two sides (or the extension lines of both sides), the corresponding line segment obtained is _________.

3. A straight line parallel to one side of a triangle and intersecting the other two sides, the corresponding side of the triangle intercepted by the original triangle ______.

1. (4 points) As shown in the figure, AB∥CD∥EF, then the following conclusion is correct ()

A.AD/DF＝BC/CE　B.BC/CE＝DF/AD

C.CD/EF＝BC/BE D.CD/EF＝AD/AF

2. (4 points) In △ABC, D and E are points on AB and AC respectively, and DE∥BC, then which of the following conclusions is incorrect ()

A.AD/DB＝AE/EC B.AB/DB＝AC/EC

C.AD/AB＝AE/AC D.AD/DB＝AC/BC

3. (4 points) As shown in the figure, it is known that straight lines a∥b∥c, straight lines m, n intersect with a, b, and c respectively at points A, C, E, B, D, F, AC=4, CE=6, BD=3, then BF=()

A． 7

B． 7.5

C. 8

D. 8.5

【Integrated use】

14. (20 points) As shown in the figure, AC∥EF∥BD.

(1) Verify: AE/AD+BE/BC=1;

(2) Verify: 1/AC+1/BD=1/EF;

(3) If AC=3, EF=2. Find the value of BD.

14.(1)∵EF∥BD, ∴AE/AD=AF/AB, and ∵EF∥AC,

∴BE/BC＝BF/AB，∴AE/AD＋BE/BC＝AF/AB＋BF/AB＝AB/AB＝1

(2)∵EF∥AC, ∴EF/AC=BF/AB, and EF∥BD,

∴EF/BD＝AF/AB, ∴EF/AC＋EF/BD＝BF＋AF/AB＝1,

∴1/AC＋1/BD＝1/EF

(3) From (2), we can get BD=6

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For more information about the PPT courseware "Parallel Lines Divide Line Segments into Proportions", please click the Parallel Lines Divide Line Segments into Proportions ppt tag.

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Update Time: 2024-09-08

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