ratio
proportional line segment (6 photos)
proportion, the general specified terminology in the technical drawing, refers to the corresponding elements of graphics and their real objects. The ratio of linear dimensions. It is shown that two ratios are called ratings, such as 3: 4 = 9: 12, 7: 9 = 21: 27in 3: 4 = 9: 12, where 3 and 12 are called external items. 4 and 9 are called the proportion. The four numbers of proportion cannot be 0.
The proportion has four items, which are two intra items and two foreign items; in 7: 9 = 21: 27, in which 7 and 27 are called foreign items, 9 and 21 are called proportions. Internal item.
There are four items, which are two intra items and two foreign items, respectively.
If the same length unit is selected, the lengths of the two lines AB are selected, the lengths of the CD are M, N, respectively, the ratio of these two line segments is the ratio of their length, ie AB: CD = m: N Among them, the line segments AB, the CD are called the front and rear items of this line segment ratio, and if m: n is indicated to the ratio K, then AB: CD = K, or AB = k · CD. The ratio of the two line segments is actually the ratio of two numbers.
Basic Concept
1. The length ratio of the 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, D. The relationship is A: B = C: D, then the four line segments are called a proportional line segment, referred to as a proportional line segment .
3. Generally, if three numbers A, B, C satisfy the proportional formula A: B = B: C, then b is called A and C proportional items.
4.d is the fourth proportion.
If A: B = C: D (BD ≠ 0), there is
1) AD = BC
2) B: a = D: c (ac ≠ 0)
3) A: c = b: D; C: a = d: b
4) (A + B): b = (C + D): D
5) A: (a + b) = C: (C + D) (A + B ≠ 0, C + D ≠ 0)
6) (AB): (A + B) = (CD): (C + D) (A + B ≠ 0, C + D 0)
7) If there is a + b = C + D Then A = C, B = D
Proof Process
as shown below
order A: B = C: D = K,
∵A: B = C: D
∴A = BK; c = DK
1) ∴AD = BK * D = KBD; BC = B * DK = KBD
∴AD = BC
2) Obviously B: a = d: c = 1 / k
3) A: C = BK: DK = B: D Binding properties 2 have c: a = d: b
4) ∵A: B = C: D
∴ (A / B) + 1 = (C / D) +1
∴ (A + B) / B = (C + D) / D = 1 + K; ie (A + B): b = (C + D): D
A + B ≠ 0, C + D ≠ 0, combined with properties 2 having b: (a + b) = D: (C + D)
and B / (a + b) = D / (C + D) = 1 / (k + 1) ... 1
5) ∵B / (A + B) = D / (C + D)
∴1- b / (a + b) = 1- D / (C + D) = 1-1 / (k + 1)
∴A / (A + B) = C / ( C + D) = k / k + 1 ... 2, A: (A + B) = C: (C + D)
A + B ≠ 0, C + D ≠ 0, combined Nature 2 has (A + B): a = (C + D): C
6) 2-1, equation two sides simultaneously (AB) / (a + b) = (CD ) / (C + D) = (k-1) / (k + 1)
7) According to (4) available A = C, B = D
proportional properties
ratio of basic properties: A / B = C / D AD = BC
ratio of comparative properties: A / B = C / D (A + B) / b = (C + D) / D
(Note: Adding Deliners on Molecules)
ratio of ratios: A / B = C / D (AB) / b = (CD) / D
ratio in ratio: if A / B = C / D = ... = m / N (B + D + ... + n ≠ 0),
(A + C + ... + M) / (B + D + ... + N) = A / B = C / D ... = m / n
ratio in the ratio of the inverse properties: A / B = C / DB \ A = D \ c
ratio is more resistant: if A / b = c / d, A / C = B / D
< B> proportional line segment: If the 4 line segment is proportional, the 4 line segment is called the proportional line segment
[ parallel line Subline segment proportional]
2 linear section 3 parallel lines, the corresponding line segment is proportional
When L1, L2, L3 is parallel to each other, AB: BC = DE: EF, AD: BE = BE: CF
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