Honors Geometry 09/9/10

Hello classmates,

Today's relatively short lesson in Honors Geometry emphasized on Collinearity, Betweenness, & Assumptions.

*Collinearity

Let us review some relevant terms:

1) Collinear - Points that lie on the same line.

2) Non-collinear - Points that do not lie on the same line.

*Betweenness

To determine whether a point is between two other points, all three points must be collinear.

Another important subject that is related to the betweenness of points is: Triangle Inequality...

When one has 3 points, there are 2 possibilities:

1) They are either collinear (When one point is between the other two, the two distances must add up to the third).

Example:

___ __ __

ABC = 20 Units... AB = 15 Units... BC =5 Units

15 Units + 5 Units = 20 Units (Point B is Collinear)

.............................. OR ....................................

2) They are non-collinear (3 points that determine a triangle).

Example:

Triangle ABC has sides of 7 Units, 10 Units, and 14 Units. Notice that 7 + 10 > 14 Units.

A triangle is non-collinear when the sum of any two side lengths is greater than the length of the third side length (^).

*Assumptions

One must never assume when looking at a diagram. Diagrams have the possibility of cheating your eyes. One must follow specific guidelines when assuming...

One should always assume:

1) Straight lines and angles

2)Collinearity of points

3) Betweenness of points

4) Relative positions of points

One should not assume:

1)Right angles

2) Congruent segments

3) Congruent angles

4) Relative sizes of segments and angles

I would like to thank everyone who has read my post on collinearity, betweenness, & assumptions.

Sincerely,

Nikita Dyatlov