# How to compare the segments?

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What does it mean to compare two segments? This means comparing their lengths, determine which of them is longer (or shorter). If there is a ruler at hand, there is nothing easier: to measure with it the lengths of both segments, and it will immediately become clear which is longer. Below, we'll tell you what to do if the ruler is not near you.

## How to compare two segments without a ruler

If the segments are drawn on cells, you cancount the cells. But this is not always so lucky. In the absence of cells, you can use the compass. First you need to install the solution of the compass at the ends of one segment, and then, without moving its legs, place the needle at the end of the other segment and see if the circulation is wider than the second segment, or already.

If there is not a compass, you can make a similarityrulers from a strip of paper. It is not necessary to draw divisions on it, it is enough to designate the beginning and end of one segment, then combine one mark with the beginning of the second segment and compare it.

So you can compare even the segments drawn onland, for example, in order to designate places for columns under the bench at equal distances from the wall of the house. Only in this case it will be necessary to use not a piece of paper, but a board or a rope.

## How to compare two segments in a grid

To compare segments, you need to know their lengths. In the article How to find the length of a segment, we explained how to find the length of a segment if its coordinates on the plane or in space are indicated. We take segments in the plane with coordinates: the segment a = {x 1, y 1; x 2, y 2} and the segment b = {x 3, y 3; x 4, y 4}.

Of course, and so it is clear that the second segment is shorterfirst, but in mathematics "seen" does not count, it is necessary to prove. Therefore, we will write a formula for calculating the lengths of segments and give the coordinates numerical values. After that, you can easily explain how to compare the two segments.

- The length of the segment a d1 = √ ((x 1 - x 2) ² + (from 1 to 2) ²)
- The length of the segment b d2 = √ ((х 3 - х 4) ² + (for 3 - у 4) ²)

Suppose that x1 = -6, y1 = 5; x 2 = 4, y 2 = -3; x 3 = -2, y 3 = -4; x 4 = 1, y 4 = -2. Hence:

- d1 = √ ((x1 - x2) ² + (for 1 - for 2) ²) = d1 = √ (((- 6) - 4) ² + (5 - (-3)) ²) = √ (-10) ² + 8 ²) = √164
- d2 = √ ((х 3 - х 4) ² + (у 3 - у 4) ²) = √ (((- 2) - 1) ² + ((-4) - (-2)) ²) = √ ((-3) ² + 2²) = √13
- √164> √13, which means that d1> d2.

Similarly, we can compare segments in three-dimensional coordinates, only then we need to take into account the third coordinates: the segment a = {x 1, y 1, z 1; x 2, y 2, z 2} and the segment b = {x 3, y 3 , z 3; x 4, y 4, z 4}.

The formulas are similar to what we wrote for the grid on the plane:

- The length of the segment a d1 = √ ((x 1 - x 2) ² + (from 1 to 2) ² + (z 1 - z 2) ²)
- The length of the segment b d2 = √ ((х 3 - х 4) ² + (for 3 - for 4) ² + (z 3 - z 4) ²)

Suppose that x1 = -6, y1 = 5, z1 = 1; x 2 = 4, y 2 = -3, z 2 = 2; x 3 = -2, y 3 = -4, z 3 = 3; x 4 = 1, y 4 = -2, z 4 = -11.

Hence:

- d1 = √ ((x1 - x2) ² + (for 1 - for 2) ² + (z 1 - z 2) ² = √ (((- 6) - 4) ² + (5 - (-3) ) ² + (1 - 2) ²) = √ ((-10) ² + 8² + (-1) ²) = √165
- d2 = √ ((х 3 - х 4) ² + (in 3 - in 4) ² + (z 3 - z 4) ²) = √ (((- 2) - 1) ² + ((-4) - (-2)) ² + (3 - (-11)) ²) = √ ((-3) ² + 2 ² + 14 ²) = √ (9 + 4 + 196) = √209
- √209> √165

Hence, in this case the second segment turned out to be greater than the first.