الهندسة والحساب المثلثي
SAT الموضوع 8 4:38 سرد باللغة الإنجليزية · ترجمة مدمجة بالإنجليزية + الصينية
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النص الصوتي
A scale factor k changes every corresponding length.
比例因子 k 会改变所有对应的长度。
A sub 2 equals k squared times A sub 1, and V sub 2 equals k cubed times V sub 1 for similar shapes.
对于相似图形，A₂ = k²A₁ 且 V₂ = k³V₁。
If k equals three halves and A sub 1 equals twenty-four square centimetres, then A sub 2 equals three halves squared times twenty-four square centimetres, which is fifty-four square centimetres.
若 k = 3/2 且 A₁ = 24 cm²，则 A₂ = (3/2)² × 24 cm² = 54 cm²。
Changing only one dimension does not justify these similarity rules.
仅改变一个维度不能使这些相似规则成立。
Each task gives its own data.
每个任务都有其自身的数据。
Do not copy the worked example’s numbers.
请勿照搬例题中的数值。
Pause here and attempt the task before revealing the reasoning.
请先暂停，完成这道原创练习再继续。
Use the full context on the preceding pages.
请利用前几页的完整背景信息。
The scale factor k is the square root of 216 over 96, which is three halves.
比例因子 k 等于九十六分之二百一十六再开方，即二分之三。
Volume uses the cube, so the new volume is three halves cubed times 160 cubic centimetres, which is 540 cubic centimetres.
体积要用立方，所以新体积等于二分之三的立方乘一百六十立方厘米，即五百四十立方厘米。
Using the area ratio directly would give the wrong volume.
直接用面积比会得到错误的体积。
Pause here and attempt the task before revealing the reasoning.
请先暂停，完成这道练习后再查看解析。
Use the full context on the preceding pages.
请结合前几页的完整背景信息。
b is the square root of 13 squared minus 5 squared, which is 12 centimetres.
b 等于十三的平方减五的平方再开方，即十二厘米。
The area is a b over 2, which is 5 times 12 over 2, or 30 square centimetres.
面积等于 ab 除以二，即五乘十二除以二，等于三十平方厘米。
Sine theta is a over c, which is 5 over 13.
sin θ 等于 a 除以 c，即十三分之五。
Pause here and attempt the task before revealing the reasoning.
请先暂停，完成这道原创练习再继续。
Use the full context on the preceding pages.
利用前几页的完整背景信息。
The third angle is 180 minus 42 minus 73, which is 65 degrees.
第三个角是一百八十减四十二减七十三，等于六十五度。
Its adjacent exterior angle is 180 minus 65, which is 115 degrees, also equal to 42 plus 73.
与它相邻的外角是一百八十减六十五，等于一百一十五度，也等于四十二加七十三。
Angles establish shape, not scale; similar triangles can have different side lengths.
角确定形状，但不确定大小；相似三角形的边长可以不同。
Pause here and attempt the task before revealing the reasoning.
请先暂停，完成这道原创练习再继续。
Use the full context on the preceding pages.
请利用前几页的完整背景信息。
Parallelism gives the matching corresponding angle, 68 degrees.
由平行得到对应的同位角是六十八度。
The adjacent pair forms a straight angle, so the other angle is 180 minus 68, which is 112 degrees.
相邻的两个角组成平角，所以另一个角是一百八十减六十八，等于一百一十二度。
Equal corresponding angles require the stated parallel lines; the straight-angle sum uses adjacency on one line.
同位角相等需要题目给出的平行线；平角之和用的是同一直线上的相邻关系。
A similar-looking sketch without parallelism would not justify the first equality.
一张看起来相似但没有平行条件的草图，不能证明第一个等式。
Return to the task and explain why the method fits.
回到该任务，并解释为何此方法适用。
Original practice does not predict an official score.
原始练习无法预测正式成绩。
Complete required live or recorded evidence separately.
请单独完成所需的现场或录制证据。
Pause and test yourself. Cover the worked answer, rebuild the answer to the last example in your own words, and name one condition that would change it before you check.
暂停一下，自我检测：遮住示范答案，用自己的话重做最后一个例子的答案，并在核对之前说出一个会改变结论的条件。