Lesson 2.1 Subsets of Lines pp. 42-44

Objectives: 1. To define important subsets of lines. 2. To apply the Line Separation Postulate. 3. To use correct notation for subsets of lines.

Definition A half-line is the set of all points on a line on a given side of a given point of the line.

A half-line does not include the point from which the half-line originates. Denoted: AB

Postulate 2.1 Line Separation Postulate. Every point divides any line through that point into three disjoint sets: the point and two half-lines.

Definition A ray is the union of a half-line and its origin. It extends infinitely in one direction from a point.

A ray includes the point from which it originates. Denoted: AB

The endpoint is always written first when naming a ray. Denoted: AB

Example: Refer to the figure to find XY  {X}. 1. { } 2. X 3. XY 4. XY 1. { } 2. X 3. XY 4. XY W X Y Z

Example: Refer to the figure to find XY  YZ. 1. XY 2. YZ 3. XY 4. XY W X Y Z

Example 1: Name five different lines. K L M E D B H I J C G F P N Example 1: Name five different lines.

Example 2: Give two other names for ID. K L M E D B H I J C G F P N Example 2: Give two other names for ID.

Example 3: Name six rays on KP. D B H I J C G F P N Example 3: Name six rays on KP.

Example 4: Name six half-lines with endpoint B. K L M E D B H I J C G F P N Example 4: Name six half-lines with endpoint B.

Example 5: Name five half-lines containing B. K L M E D B H I J C G F P N Example 5: Name five half-lines containing B.

Homework pp. 43-44

►A. Exercises Use the figure below for exercises 4-10. A B C D 5. How many sets are formed on AD by the point C? Name them.

►A. Exercises Use the figure below for exercises 4-10. A B C D 7. Explain why BC and BD are the same ray.

►A. Exercises Use the figure below for exercises 4-10. A B C D 7. Explain why BC and BD are the same ray.

►A. Exercises Use the figure below for exercises 4-10. A B C D 9. Name AC in two other ways.

►B. Exercises Use the figure below for exercises 11-18. A B C D 11. Find AB  {A} = AB

►B. Exercises Use the figure below for exercises 11-18. A B C D 13. CD  CA = { }

►B. Exercises Use the figure below for exercises 11-18. A B C D 15. AC  BC = BC

►B. Exercises Use the figure below for exercises 11-18. A B C D 17. BD  CA = AD

20. Name as many rays as possible in the figure. ►C. Exercises 20. Name as many rays as possible in the figure. A I H B G F C D E

■ Cumulative Review Identify the undefined term best illustrated in each example. 21. a piece of paper

■ Cumulative Review Identify the undefined term best illustrated in each example. 22. an electron

■ Cumulative Review Identify the undefined term best illustrated in each example. 23. a crease in a garment

■ Cumulative Review Identify the undefined term best illustrated in each example. 24. a ramp for loading a truck

■ Cumulative Review Identify the undefined term best illustrated in each example. 25. a pixel (smallest dot on a computer screen)