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Lines and Line Segments Ch 1-3 C. N. Coln Geometry St. Barnabas H. S. Bronx, NY

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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

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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

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The length or measure of a line segment is the distance between its endpoints.

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-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

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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|

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-5 -4 -3 -2 -1 0 1 2 3 4 5 6 AB |(-3) 4 |= | -3 + -4 |= | -7 |= 7 | 4 (-3) | = | 4 + 3 | = | 7 |= 7

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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

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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.

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p. 10 # 3-17 (e)