Collinearity, Betweeness, and Assumptions

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# Collinearity, Betweeness, and Assumptions - PowerPoint PPT Presentation

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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### Collinearity, Betweeness, and Assumptions

Lesson 1.3

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

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

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.

Assumptions from diagrams:

Can assume:

Straight lines

Straight angles

Collinear points

Betweenness of points

Relative position of points

Can’t Assume!

Right angles

Congruent segments

Congruent angles

Relative size of angles

Relative size of segments

Example:

B

D

A

C

E

Assume:

C, D, E non-collinear

C is between B and E

E is to the right of A

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