Basic Geometric 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?

Select all that apply

A
only one
B
two
C
three
D
an infinite number

Check my answer (3)

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

Select all that apply

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

Check my answer (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?

Select all that apply

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.

Check my answer (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?

Select all that apply

A
Yes
B
No

Check my answer (3)

Can two lines intersect at 1 point?

Select all that apply

A
Yes
B
No

Check my answer (3)

Can two lines intersect at 2 points?

Select all that apply

A
Yes
B
No

Check my answer (3)

Can two lines intersect at an infinite number of points?

Select all that apply

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

Check my answer (3)

Postulate #2: The Line Intersection Postulate

Which of the following best describes the postulate.

Select all that apply

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.

Check my answer (3)

Postulate #3: The Parallel Construction Postulate

Consider the following as you examine the applet below. What if I wanted to draw a new line that contains point C and is parallel to the line shown below? How many different new lines could I draw that satisfy these conditions?

Postulate #3: Parallel Construction Postulate

Which of the following is true?

Select all that apply

A
Through a point not on a line, there is no parallel to the original line that can be drawn.
B
Through a point not on a line, there are an infinite number of distinct parallels to the original line that can be drawn.
C
Through a point not on a line, there is exactly one distinct parallel to the original line that can be drawn.

Check my answer (3)

Constructing parallel lines.

You can construct a parallel line automatically using Geogebra. In the toolbar of the Geogebra applet, click on the fourth box from the left and select this (the Parallel line tool). Then click on the line (in the middle away from the points) and then click on Point C.

Basic Geometric 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

Postulate #3: The Parallel Construction Postulate

Postulate #3: Parallel Construction Postulate

Constructing parallel lines.

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