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Collinearity, Betweeness, and Assumptions. Lesson 1.3. Col line ar: points on the same line. Points ABC are collinear. A. B. C. Non-collinear: points that do not lie on the same line. B. A. You can connect AB, AC, or BC, but ABC does not form a line. C. Betweeness of Points:.

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slide2

Collinear: points on the same line

Points ABC are collinear

A

B

C

Non-collinear: points that do not lie on the same line

B

A

You can connect AB, AC, or BC, but ABC does not form a line.

C

slide3

Betweeness of Points:

To have betweeness of points, all points must be on the same line.

Z

Y

X

Z is between Y and X

Y

Z

X

X is not “between” Y and Z

slide4

Two possibilities with 3 points

Collinear: all points are on the same line.

Triangle : makes a triangle.

Triangle Inequality

The sum of two side lengths is always greater than the third side.

slide5

Assumptions from diagrams:

Can assume:

Straight lines

Straight angles

Collinear points

Betweenness of points

Relative position of points

slide6

Can’t Assume!

Right angles

Congruent segments

Congruent angles

Relative size of angles

Relative size of segments

slide7

Example:

B

D

A

C

E

Assume:

AD and BE straight lines

C, D, E non-collinear

C is between B and E

E is to the right of A

slide8

B

D

A

C

Can’t Assume:

<BAC is a right angle

CD = DE

<B = <E

<CDE is obtuse

BC is longer than CE

E