Basic Geometric Postulates 25
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: TWO POINT 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 blue 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?
To name a line using points I should use...
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, "lines" in geometry means STRAIGHT paths with no curves).
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. Try to draw a line through all three points.
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?
within the line menu and then click on various points. You can undo your work with the UNDO icon in the upper right. Try to draw a line through all three points.
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: Two Point Postulate
Which of the following best describes the Two Point Postulate?
Postulate #2: The Line Intersection Postulate
For this postulate we will consider two lines.
Drag the various blue 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?
Can two lines intersect at 1 point?
Can two lines intersect at 2 points?
Can two lines intersect at an infinite number of points?
Postulate #2: The Line Intersection Postulate
Which of the following best describes the postulate.
Postulate #3: Plane-Line Postulate
For this postulate, we will consider the position of two points on a line.
Use the POINT tool to add two points to plane. Click the point A button, then click anywhere in the grey parallelogram. Use the MOVE tool 
to click and drag the plane and check the position of the points. ,
Then use the LINE tool to draw a line through the two points you created.
Where is the line's position on the plane? Can you draw the line so that it is on the plane? Can you draw the line so that it is intersecting the plane, but not on it? Can you draw the line off the plane?
to click and drag the plane and check the position of the points. ,
Then use the LINE tool to draw a line through the two points you created.
Where is the line's position on the plane? Can you draw the line so that it is on the plane? Can you draw the line so that it is intersecting the plane, but not on it? Can you draw the line off the plane?Plane
Postulate #3: Plane-Line Postulate
Which of the following best describes the postulate?