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Describe the process of finding the length of a segment with given endpoints on a number line.
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Subtract the coordinates of the endpoints, take the absolute value of the result.
If LM = 7y + 9, MN = 3y + 4, and LN = 143, how do you solve for y?
Combine the segments: 7y + 9 + 3y + 4 = 143, then solve for y: 10y + 13 = 143, y = 13.
How do you determine the congruence of segments on a coordinate grid?
Calculate the length of each segment using the absolute value of differences in coordinates and compare them.
Calculate the length of segment AC if AB = 12 and BC = 19.
The length of AC is 31, because AB + BC = 12 + 19 = 31.
How do you verify if a point is 'between' two other points?
A point is 'between' two other points if all three are collinear.
Solve for x given that AB = 8, BC = x, and AC = 23.
x = 15, because 8 + x = 23, so x = 23 - 8.
Define congruent segments and give their notation.
Congruent segments have the same length and are denoted with the ≅ symbol.
What steps would you take to solve for y in an algebraic segment addition problem?
Combine like terms, set the equation equal to the total segment length, and solve for y.
How do you confirm if two segments on a number line are congruent?
Calculate the length of each using the Ruler Postulate, and if they are equal, the segments are congruent.
What distinguishes a line from a segment?
Lines extend indefinitely and cannot be measured, while segments have endpoints and can be measured.
According to the Segment Addition Postulate, what is the relationship between segment parts and the whole?
If point B is between A and C, then the length of AB plus the length of BC equals the length of AC.
Determine if segments JK and LM are congruent if JK is horizontal with coordinates (-3, 2) and LM is vertical with coordinates (3, -2).
JK and LM are congruent, with both having a length of 5.
What condition must be satisfied for three points to be collinear in the context of a point being 'between' two others?
All three points must lie on the same straight line.
How would you solve for a missing segment length using the segment addition postulate?
Set up an equation where the sum of the known segments equals the total segment length, then solve for the missing value.
What is the Ruler Postulate?
The distance between two points is the absolute value of the difference of their coordinates.
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