"Perpendicular Lines" Intersecting Lines and Parallel Lines PPT Courseware 4

Description

"Perpendicular Lines" Intersecting Lines and Parallel Lines PPT Courseware 4

think

Someone accidentally fell into a lake with crocodiles. As shown in the picture, he is at point P. What route should he choose to swim to the shore m as soon as possible?

Thinking: What is the difference between "vertical line" and "vertical line segment"?

1. Among all the line segments connecting a point outside the straight line and every point on the straight line, the perpendicular segment is the shortest.

Simply put: the vertical line segment is the shortest.

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

Apply what you learn

Multiple choice questions

It is known that P is a point outside the straight line a, then which of the following statements is correct: ( )

(A) Draw a perpendicular to a through point P. The vertical foot is D. Straight line PD is the distance from point P to straight line a.

(B) Draw the perpendicular segment PD of a through point P, then PD is the distance from point P to straight line a.

(C) Draw a straight line through point P and intersect a at D. Then the length of line segment PD is the distance from point P to straight line a.

(D) Draw the perpendicular segment PD of a through point P. Then the length of segment PD is the distance from point P to straight line a.

As shown in the figure, points M and N are on straight lines AB and CD respectively. Use a triangle to draw the figure.

1) The perpendicular line drawing CD through point M intersects CD at point F,

2) The distance between point M and point N is the length of the line segment ____,

3) The distance from point M to CD is the length of the line segment ____.

As shown in Figure 2-22, AC⊥BC is at C, CD⊥AB is at D, and DE⊥BC is at E. Try to compare the sizes of four line segments AC, CD, DE and AB

Solution: ∵ AC⊥BC in C, (known)

∴AC＜AB. (Property 2 of vertical lines)

And ∵ CD⊥AD in D, (known)

∴ CD＜AC. (Property 2 of vertical lines)

∵ DE⊥CE in E, (known)

∴DE＜CD. (Property 2 of vertical lines)

∴ AB＞AC＞CD＞DE．

Multiple choice questions:

As shown in the figure, AC⊥BC, ∠C=900, the shortest line segment AC, BC, CD is ( )

(A) AC (B) BC (C) CD (D) Unsure

summary

Recall the knowledge about the intersection of two straight lines and ask: Can you draw them into a knowledge structure diagram?

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Update Time: 2024-11-22

This template belongs to Mathematics courseware People's Education Press Seventh Grade Mathematics Volume 2 industry PPT template

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