The definition of the ratio of the line segment, the nature of the proportional line segment

Definition of the ratio of line segments: The ratio of the length of two line segments in the same unit length is called the ratio of the two line segments.

Definition of proportional segments: Of the four segments, if the ratio of two of the segments is equal to the ratio of the other two segments, then the four segments are called proportional segments.

1. Generally speaking, it is more convenient to use the line scale to find the actual distance between two places than the digital scale.

2. The distance from Nanjing to Beijing is 15 centimeters measured on a map with a scale of 1 5000000, and the actual distance from Nanjing to Beijing is about 15 kilometers. Whether it is the method of finding the latter term of the ratio (i.e., using the distance scale on the graph = actual distance) or the method of solving the proportion, the actual distance is calculated in "centimeters", and it is also calculated as "kilometers". This is more troublesome, and it is easy to write the wrong name of the unit, or make mistakes in the calculation process.

If you attach a line segment scale like the one above to the map, you can see that the distance of 1 cm on the map is equivalent to the actual distance of 50 kilometers on the ground. Then, the actual distance of 15 centimeters measured on the map is 15 50 kilometers, which can be directly calculated by multiplication, and the column equation is:

50 15 = 750 (km).

3. When calculating the line segment scale, the actual length of the line segment scale must be measured first, and then calculated.

The basic nature of proportion: a b = c d

Proportional properties of the AD=BC ratio: a b = c d

a+b)/b=(c+d)/d

Note: Add the denominator on the numerator).

Proportional properties: a b = c d

a-b)/b=(c-d)/d

Proportional nature of proportions: if.

a/b=c/d=…=m/n(b+d+…+n≠0), then.

a+c+…+m)/(b+d+…+n)=a/b=c/d…Inverse property of the ratio of = m n: a b = c d

b\a=d\c

Proportions are more than nature: if.

a/b=c/d

Rule. a/c=b/d

Proportional line segments: If the 4 line segments are proportional, the 4 line segments are called proportional line segments.

Parallel lines divide segments proportionally].

2. If you cut 3 parallel lines in a straight line, the corresponding line segments are proportional.

When L1, L2, and L3 are parallel to each other, ab:bc=de:ef,ad:be=be:cf

Apply] the scale of the map.

If so, let's say that these four numbers are proportional.

a:b=c:d→ad=bc。(can also be reversed).

If a:b=c:d, then (a b):b=(c d) :d

If a:b=c:d=·· m:n（b+d+·· n≠0), then (a+c+·· m）:（b+d+·· n）=a:b

1.The length ratio of two line segments is called the ratio of these two line segments.

2.Under the same unit, the length of the four line segments is a, b, c, and d, and their relationship is a:b=c:d, then, these four line segments are called proportional line segments, referred to as proportional line segments.

3.In general, if the three numbers a, b, and c satisfy the proportional formula a:b=b:c, then b is called the proportional term of a,c. (It is not difficult to see that at this time b 2 = ac, that is, b is the geometric mean of ac at this time).

It's called the fourth proportional term a, b, and c. (At this time, a, b, c are written sequentially, and must be written in order, if b:a=c:d, then d should be written as the fourth proportion of b, a, c).

5.A:B=C:D; a:c=b:d;d:b=c:a and d:c=b:a

6.If a:b=c:d, then (a b):b=(c d) :d

7.If a b=c d=....=m∶n

b+d+…+n≠0 , then a+c+....+m﹚∶﹙b+d+…+n﹚=a∶b

If the four line segments a, b, c, and d satisfy a b=c d, then the four line segments a, b, c, and d are called proportional segments. (There is a precedence, not reversed), ABCD cannot be 0. It is meaningless to be 0.

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1.It is known that the line segments a=3cm, b=5cm, c=7cm, and the fourth term x of a, b, and c

x=bc÷a=35÷3=35/3cm

2.Knowing x: search branch line y: tie bi z=3:5:6, and 2x-y+3z=38, find the value of 3x+y-2z.

Let x:y:z=3:5:6 k

then x=3k, y=5k, z=6k

2x-y+3z=38=6k-5k+18k

k=23x+y-2z=9k+5k-12k=2k=43.Knowing x:2=3:4, then x= 2x3 4=

Takeaway x = 9 set up a feast x = 3x y = 5x z = 6x6x-5x + 18x = 38

x=23x+y-2z=9x+5x-12x=4x=3 Absolute silver4 *2=3 2