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Authoritative PPT Summary
"Proportional Line Segment" PPT courseware
1. Among the four line segments a, b, c, d, if the ratio of a to b is equal to the ratio of c to d, that is, _________, we call these four line segments ___________, or _________ for short.
2. Basic properties of proportion: if a/b=c/d, then a/d=______; if a/b=b/c, that is, b2=________, then b is called a, and c is _________.
1. (4 points) It is known that line segment AB=2.5 m and line segment CD=400 cm, then AB:CD=________.
2. (4 points) Line segments a, b, c, d are proportional, that is, a/b=c/d, where a=2 cm, b=4 cm, c=5 cm, then d=________.
3. (4 points) On the Nanjing traffic map with a scale of 1:38 000, the distance between Xuanwu Lake Park and Yuhuatai Martyrs Cemetery is about 20 cm, then the actual distance between them is about ()
A． 1900 cm B． 0.76 meters
C. 1.9 kilometers D． 7.6 kilometers
4. (4 points) Among the following four sets of line segments, the one that is proportional is ()
A． a=16 cm, b=8 cm, c=5 cm, d=10 cm
B． a=8 cm, b=0.05 cm, c=0.06 cm, d=10 cm
C. a=4 cm, b=8 cm, c=0.03 cm, d=0.09 cm
D. a＝3√2 cm, b＝2√3, c＝5√2 cm, d＝6√3 cm
【Error-prone Inventory】
[Example] Given that a=1, b=4, find the value of c in the ratio of a and b.
[Incorrect explanation] ∵c is the middle term in the ratio of a and b, ∴c2=ab=1×4=4, ∴c=2.
[Error Cause Analysis] Generally speaking, there are two terms in the proportion, and they are a pair of numbers that are opposite to each other, unless there are special provisions such as line segments, side lengths and other practical issues. Since a, b, and c are not specified as line segments, c can take a negative value.
17． (9 points) It is known that point C is a point on the line segment AB, point D is a point on the extension line of AB, and AD: BD = AC: CB. It is known that AB = 6 cm, AC = 3.6 cm, find AD, BD long.
17.BD＝12 cm，AD＝18 cm
【Integrated use】
18. (10 points) It is known that △ABC has three sides a, b and c.
Foot (a-c): (a+b): (c-b)=-2:7:1, and a+b+c=24 cm.
(1) Find the values of a, b, c;
(2) Determine the shape of △ABC.
(1)a=6 cm, b=8 cm, c=10 cm
(2) Because a2+b2=62+82=100, c2=102=100, so a2+b2=c2, so △ABC is a right triangle
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