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The line and its parts
In geometry, lines are considered to be infinite. They are denoted by lowercase letters.
Several lines can be drawn through a point.
\latex{ E }
\latex{ e }
\latex{ f }
\latex{ g }
Exactly one line can be drawn through two points.
\latex{ K }
\latex{ L }
Point \latex{ P } is on line \latex{ f } : point \latex{ P } is part of line \latex{ f }. Point \latex{ R } is not on line \latex{ f } : point \latex{ R } is not part of line \latex{ f }.
\latex{ P }
\latex{ R }
\latex{ f }
Half line or rays
If we take line \latex{ e } and mark point \latex{ P } on it, \latex{ P } will divide the line into two rays (also called half-lines).
Unless stated otherwise, point \latex{ P } is part of both lines.
Unless stated otherwise, point \latex{ P } is part of both lines.
\latex{ e }
\latex{ P }
\latex{ f }
Segments
To turn line \latex{ e } into a segment, you need to create a bounded section of it by marking two points on it. These endpoints are points \latex{ A } and \latex{ B } in this example. Segment \latex{ c } can also be denoted as segment \latex{ AB } by its two endpoints.
The length of segment \latex{ AB } is the same as the distance between points \latex{ A } and \latex{ B }.
The length of segment \latex{ AB } is the same as the distance between points \latex{ A } and \latex{ B }.
\latex{ e }
\latex{ c }
\latex{ A }
\latex{ B }
\latex{ F }
\latex{ b }
\latex{ C }
\latex{ D }
\latex{ a }
\latex{ E }
Segment \latex{ c } can be designated by its two endpoints: segment \latex{ AB }.
The length of segment \latex{ AB } is called the distance between points \latex{ A } and \latex{ B }.
The length of segment \latex{ AB } is called the distance between points \latex{ A } and \latex{ B }.
Exercises
{{exercise_number}}. Draw the points on graphing paper as seen in the images below and draw all the possible lines that pass through at least two points. How many lines have you drawn?
\latex{ A }
\latex{ B }
\latex{ C }
\latex{ D }
\latex{ E }
a)
\latex{ A }
\latex{ B }
\latex{ C }
\latex{ D }
\latex{ E }
\latex{ F }
b)
{{exercise_number}}. Draw \latex{ 5 } points in a way that
a) there are exactly \latex{ 3 } points on a line;
b) all the points are on a line;
c) there are exactly \latex{ 4 } points on a line;
d) no more than \latex{ 2 } points are on a line.
{{exercise_number}}. We marked the points \latex{E}, \latex{F}, \latex{G} and \latex{H} on the line \latex{f} as seen in the image.
\latex{ E }
\latex{ f }
\latex{ F }
\latex{ G }
\latex{ H }
a) What is the common part of the ray starting with \latex{ E } and containing \latex{ F }, and the ray starting with \latex{ G } and containing \latex{ E }?
b) What is the common part of the ray starting with \latex{ E } and containing \latex{ F } and the ray starting with \latex{ F } and containing \latex{ G }?
b) What is the common part of the ray starting with \latex{ E } and containing \latex{ F } and the ray starting with \latex{ F } and containing \latex{ G }?
{{exercise_number}}. Points \latex{ A }, \latex{ B }, \latex{ C } and \latex{ D } are marked on line \latex{ e }.
\latex{ e }
\latex{ A }
\latex{ B }
\latex{ C }
\latex{ D }
a) What is the common part of segments \latex{AC} and \latex{BD}?
b) What is the common part of segments \latex{AB} and \latex{DB}?
c) What kind of loci do the points of degments \latex{AC} and \latex{BD} form together?
{{exercise_number}}. What is the length of segments \latex{ AE } and \latex{ DE } if
a) \latex{ AC = 5\,cm, BE = 10\,cm, CD = 4\,cm } and \latex{ BC = 2\,cm };
b) \latex{ AD = 5\,cm, BE = 7\,cm, CD = 2\,cm } and \latex{ BD = 4\,cm ?}
b) \latex{ AD = 5\,cm, BE = 7\,cm, CD = 2\,cm } and \latex{ BD = 4\,cm ?}
\latex{ A }
\latex{ B }
\latex{ C }
\latex{ D }
\latex{ E }
{{exercise_number}}. Which of the following statements are true and which are false?
If there are two rays located on a line, then they
a) must have a common point;
b) may have a common point;
c) do not have any common points;
d) may have an infinite number of common points.
{{exercise_number}}. Andy, Ben, Clare, Dan and Erika live on the same side of a straight road (in that order). There is a tree in front of each of their houses: the trees in front of Andy and Erika are \latex{ 90\,m } apart, the trees in front of Erika and Clare are \latex{ 60\,m } apart, the trees in front of Dan and Erika are \latex{ 28\,m } apart, and the trees in front of Dan and Ben are \latex{ 58\,m } apart. How far is Andy's tree from Ben's tree?
Quiz
The Smiths from Sevenville are discussing their visit to their relatives:
Dad: We left after lunch to visit Aunt Sara, but we couldn't go faster than \latex{ 20\,km } \latex{an} \latex{hour} because there was an accident at the roundabout.
Mum: Yes, but not exactly at it. We drove for another quarter of an \latex{hour} after the roundabout until we saw what had happened.
Pam: Yes, a trailer had flipped over \latex{ 2 } \latex{kilometres} away from the church in Cockooville. There were cabbages all over the road.
Granny: It was at least \latex{ 3 } \latex{kilometres!} It happened right in front of Mary's house.
Mum: Yes, but not exactly at it. We drove for another quarter of an \latex{hour} after the roundabout until we saw what had happened.
Pam: Yes, a trailer had flipped over \latex{ 2 } \latex{kilometres} away from the church in Cockooville. There were cabbages all over the road.
Granny: It was at least \latex{ 3 } \latex{kilometres!} It happened right in front of Mary's house.
Mark Mary's house on the map. Write the names of the two towns below them.
