Points/Lines Postulates

In this lesson, you will use Geogebra to explore some basic geometric postulates. When you get to a question that has the word "POSTULATE" in it, after checking your answer WRITE DOWN the correct formulation of that Postulate in your notes!

POSTULATE #1: POINT-LINE POSTULATE

Look at the figure below and consider this question: Is it possible to identify a line using only one point? If I talked about "line E" in the figure below, what line would I be talking about? Click on one of the points and drag it to see if that changes your mind.

Click and drag on a point.

If you drew as many lines as possible that pass through point E, how many lines could you draw?

적용되는 모든 것을 선택하세요.

A
only one
B
two
C
three
D
an infinite number

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To name a line using points I should use...

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A
exactly one point
B
exactly two points
C
two or more points

답안을 점검하세요 (3)

Look at the figure below and consider these questions: How many different lines could I draw that go through points A and B? How many different lines could I draw that go through points A, B and C? (remember that "lines" in geometry means STRAIGHT lines). Try clicking on the line tool within the line menu and then click on various points. You can undo your work with the UNDO icon in the upper right. Now click back on the MOVE tool and drag point C around. Can you drag it to a location where a single line could be drawn that contains points A, B and C?

Create multiple lines as instructed above.

Postulate #1: The Point-Line Postulate

Which of the following best describes the Point-Line Postulate?

적용되는 모든 것을 선택하세요.

A
Through any two points there is at least one distinct line that can be drawn.
B
Through any two points there is exactly one distinct line that can be drawn.
C
Given two points, sometimes there is no line that can be drawn that goes through both of them.
D
Through any two points there is more than one line that can be drawn.

답안을 점검하세요 (3)

Postulate #2: The Line Intersection Postulate

For this postulate we will consider two lines. Drag the various points around and consider this question: What are the possible number of points of intersection for two lines?

Drag the points as instructed above.

Can two lines intersect in no points?

적용되는 모든 것을 선택하세요.

A
Yes
B
No

답안을 점검하세요 (3)

Can two lines intersect at 1 point?

적용되는 모든 것을 선택하세요.

A
Yes
B
No

답안을 점검하세요 (3)

Can two lines intersect at 2 points?

적용되는 모든 것을 선택하세요.

A
Yes
B
No

답안을 점검하세요 (3)

Can two lines intersect at an infinite number of points?

적용되는 모든 것을 선택하세요.

A
Yes (but the two lines are really just the same line)
B
No.

답안을 점검하세요 (3)

Postulate #2: The Line Intersection Postulate

Which of the following best describes the postulate.

적용되는 모든 것을 선택하세요.

A
Distinct lines that intersect will intersect in exactly one point.
B
Lines that intersect can intersect in any number of points.
C
Any two lines will always intersect in one point, no matter what.

답안을 점검하세요 (3)

Points/Lines Postulates

POSTULATE #1: POINT-LINE POSTULATE

Click and drag on a point.

Create multiple lines as instructed above.

Postulate #1: The Point-Line Postulate

Postulate #2: The Line Intersection Postulate

Drag the points as instructed above.

Postulate #2: The Line Intersection Postulate

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