ESSENTIALS OF GEOMETRY Lines and Line Segments Ch 1-3 C. N. Colón Geometry St. Barnabas H. S. Bronx, NY
Transcript
Slide 1
Slide 2
Lines and Line Segments Ch 1-3 C. N. Coln Geometry St. Barnabas
H. S. Bronx, NY
Slide 3
Points that lie on the same line. Points A, B, and C are
collinear because they lie on the same line. Points A, B, and D are
noncollinear because they do not lie on the same line. ABC D
Slide 4
A line segment is part (subset) of a line that has a beginning
and an end. The beginning point and the ending point are called
endpoints. A line segment includes all points between the
endpoints. You name a line segment using both endpoints and put a
little line on top A B BA
Slide 5
The length or measure of a line segment is the distance between
its endpoints.
Slide 6
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 AB and that distance is the
absolute value of the difference of the coordinates of the two
endpoints
Slide 7
We add the additive inverse ! You may have heard this as
keep-change-change or keep-change-flip
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-5 -4 -3 -2 -1 0 1 2 3 4 5 6 AB The length of a segment is the
number of spaces between the endpoints on the number line. The
length of segment AB in this case is 7. To do the math the formula
is |A B| or |B A|
If point A is -4 and point B is 8, what is the length of ?
|(-4) (8)| = |(-4) + (-8)| = |-12|= 12 | (8) - (-4) | = | (8) + (4)
| = |12| = 12 AB Either way, the length of segment AB is 12.
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A B C B is between A and C iff A, B, and C are distinct
collinear points and AB + BC = AC. This is also called Betweeness.
Proof: AB + BC = (a b) + (b c) = a b + b c = a c = AC
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Congruent means almost the same thing as equal. Congruent means
having the same measure. The symbol for congruence is: BUT I SAY:
SAME SIZE SAME SHAPE
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Congruent means that two objects have the Congruent segments
are segments that have the same measure. The symbol is used to
state that two objects are congruent. A B C D = ~ AB CD = ~ Tick
marks are used to show congruence same size and same shape.
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A B C DEDE F G
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1. If two segments have the same length as measured by a fair
ruler, then the two segments are congruent. 2. CONVERSELY: if two
segments are congruent, then the two segments have the same length
as measured by a fair ruler.
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If the distance between the numbers on the line is equal, then
the line is a fair ruler -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Slide 17
5.Keeping the same opening on the compass, set the point of the
compass on the new point, and draw another mark to the right. Label
the new intersection 2. 1.Use your straightedge to draw a line.
2.Choose any point on the line and label it 0 3.Use the pencil part
of the compass to draw a short mark that crosses the number line to
the right of 0. Label the point of intersection 1. The distance
from 0 to 1 on a ruler is known as the unit length. Two common unit
lengths are inches and centimeters. Make up a name for your unit
length. Use your ruler to measure an object in the classroom.
Estimate the fractional part of the measurement. Adjust your
compass to an appropriate spacing and mark your ruler Compare your
measurement with those of your classmates. What do you observe?
6.Repeat the previous step as many times as desired, adding 1 to
the label each time.