Post on 12-Jan-2016
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Lesson 2.1 Subsets of Lines
pp. 42-44
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.
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.
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 thepoint from which the half-line originates.
A half-line does not include thepoint from which the half-line originates.
Denoted: ABDenoted: 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.
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.
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. A ray includes the point from which it originates.
Denoted: ABDenoted: AB
The endpoint is always written first when naming a ray. The endpoint is always written first when naming a ray.
Denoted: ABDenoted: AB
Example: Refer to the figure to find XY {X}. 1. { }2. X3. XY4. XY
Example: Refer to the figure to find XY {X}. 1. { }2. X3. XY4. XY
WW XX YY ZZ
Example: Refer to the figure to find XY YZ. 1. XY2. YZ3. XY4. XY
Example: Refer to the figure to find XY YZ. 1. XY2. YZ3. XY4. XY
WW XX YY ZZ
AAKK
LL MM EE
DD
BBHH
IIJJ
CC GG
FF
PPNN
Example 1:Example 1: Name five Name five different lines.different lines.
Example 2: Example 2: Give two other Give two other names for names for IDID..
AAKK
LL MM EE
DD
BBHH
IIJJ
CC GG
FF
PPNN
Example 3: Example 3: Name six rays on Name six rays on KPKP..
AAKK
LL MM EE
DD
BBHH
IIJJ
CC GG
FF
PPNN
Example 4: Example 4: Name six half-Name six half-lines with endpoint lines with endpoint BB..
AAKK
LL MM EE
DD
BBHH
IIJJ
CC GG
FF
PPNN
Example 5:Example 5: Name five half- Name five half-lines containing lines containing BB..
AAKK
LL MM EE
DD
BBHH
IIJJ
CC GG
FF
PPNN
Homeworkpp. 43-44
Homeworkpp. 43-44
AA BB CC DD
5. How many sets are formed on AD by the point C? Name them.
5. How many sets are formed on AD by the point C? Name them.
►A. ExercisesUse the figure below for exercises 4-10.
►A. ExercisesUse the figure below for exercises 4-10.
7. Explain why BC and BD are the same ray.
7. Explain why BC and BD are the same ray.
►A. ExercisesUse the figure below for exercises 4-10.
►A. ExercisesUse the figure below for exercises 4-10.
AA BB CC DD
►A. ExercisesUse the figure below for exercises 4-10.
►A. ExercisesUse the figure below for exercises 4-10.
AA BB CC DD
7. Explain why BC and BD are the same ray.
7. Explain why BC and BD are the same ray.
9. Name AC in two other ways.9. Name AC in two other ways.
►A. ExercisesUse the figure below for exercises 4-10.
►A. ExercisesUse the figure below for exercises 4-10.
AA BB CC DD
= AB= AB11. Find AB {A} 11. Find AB {A}
►B. ExercisesUse the figure below for exercises 11-18.
►B. ExercisesUse the figure below for exercises 11-18.
AA BB CC DD
= { }= { }13. CD CA13. CD CA
AA BB CC DD
►B. ExercisesUse the figure below for exercises 11-18.
►B. ExercisesUse the figure below for exercises 11-18.
►B. ExercisesUse the figure below for exercises 11-18.
►B. ExercisesUse the figure below for exercises 11-18.
15. AC BC15. AC BC = BC= BC
AA BB CC DD
►B. ExercisesUse the figure below for exercises 11-18.
►B. ExercisesUse the figure below for exercises 11-18.
17. BD CA17. BD CA = AD= AD
AA BB CC DD
►C. Exercises 20. Name as many rays as
possible in the figure.
►C. Exercises 20. Name as many rays as
possible in the figure.
AAAAIIII HHHH
BBBB
GGGG
FFFF
CCCCDDDD
EEEE
■ Cumulative ReviewIdentify the undefined term best illustrated in each example.21. a piece of paper
■ Cumulative ReviewIdentify the undefined term best illustrated in each example.21. a piece of paper
■ Cumulative ReviewIdentify the undefined term best illustrated in each example.22. an electron
■ Cumulative ReviewIdentify the undefined term best illustrated in each example.22. an electron
■ Cumulative ReviewIdentify the undefined term best illustrated in each example.23. a crease in a garment
■ Cumulative ReviewIdentify the undefined term best illustrated in each example.23. a crease in a garment
■ Cumulative ReviewIdentify the undefined term best illustrated in each example.24. a ramp for loading a truck
■ Cumulative ReviewIdentify the undefined term best illustrated in each example.24. a ramp for loading a truck
■ Cumulative ReviewIdentify the undefined term best illustrated in each example.25. a pixel (smallest dot on a computer
screen)
■ Cumulative ReviewIdentify the undefined term best illustrated in each example.25. a pixel (smallest dot on a computer
screen)