Lines and Line Segments Ch 1 3 C

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

Points that lie on the same line. ● A ● B C ● ●D 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.

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 AB A B BA

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

A -5 -4 -3 B -2 -1 0 1 2 3 4 5 6 …and that distance is the absolute value of the difference of the coordinates of the two endpoints

We add the additive inverse ! You may have heard this as keep-change or keep-change-flip

A -5 -4 B -3 -2 -1 0 1 2 3 4 5 6 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 AB ? |(-4) – (8)| = | (8) - (-4) | = |(-4) + (-8)| = | (8) + (4) | = |-12|= 12 |12| = 12 Either way, the length of segment AB is 12.

● 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

Congruent means having the same measure. The symbol for congruence is: Congruent means almost the same thing as equal. BUT I SAY: “SAME SIZE SAME SHAPE”

Congruent means that two objects have the same size and same shape. Congruent segments are segments that have the same measure. The symbol ~ = is used to state that two objects AB ~ are congruent. = CD A B C D Tick marks are used to show congruence

F A D B C E G

1. 2. If two segments have the same length as measured by a fair ruler, then the two segments are congruent…. CONVERSELY: if two segments are congruent, then the two segments have the same length as measured by a fair ruler.

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 If the distance between the numbers on the line is equal, then the line is a “fair ruler”

6. 1. Repeat the previous step Use your straightedge toas • Use your ruler to measure an many object in the times desired, 1 to draw as a line. 5. classroom. Keeping the sameadding opening onthe labelcompass, each time. the set the point of the 2. Choose any point on the line • Estimate the fractional part of the measurement. compass and your labelon it the 0 newtopoint, Adjust compass an appropriate spacing draw another mark to the right. and. Use mark your ruler 3. the pencil part of the 2. Label the new intersection Thecompass distancetofrom 0 atoshort 1 on a ruler is known as draw • Compare your measurement with those of your themark unit that length. Two common unit lengths are crosses the classmates. What do you observe? inches and line centimeters. number to the right of 0. Label the point of intersection 1. Make up a name for your unit length.

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