湘教版初中数学教材配套资源
按照湘教版初中教材，充分利用GeoGebra在线资源库相关资源，将初中数学教材配套资源收集并整理成册，以便一线教师使用。
Table of Contents
- 七年级上册
- Thermometer - Positive and Negative Numbers
- 数轴
- 相反数 思考（教材第10页）
- 可视化整数加法的副本
- 练习有理数加法
- 绝对值的含义
- 有理数的加法运算规律的探究
- Solving Equations using Balance 以天平解方程
- 两点之间线段最短
- Angle Bisector Definition (I)
- 立体图形
- Measurement & Classification of Angles 角的量度和分類
- Exploring Complementary Angles
- Complementary and Supplementary Angles: Quick Recap
- Properties of parallelogram
- 七年级下册
- Linear Equations, Systems and Problems
- 因式分解(十字相乘法)
- 平行线（转动木条）
- §1-1.平行移動
- P3练习：相交线模型
- P26信息技术应用：探究平行线的性质
- Axiom 5
- 三线八角
- P5探究：垂线段最短
- 平行直线距离
- 轴对称
- 轴对称
- 旋转
- 八年级上册
- 三角形三边关系
- Triangle Angle Theorems
- 三角形的內角
- 三角形的外角
- Axiom 1
- Axiom 2
- Axiom 3
- Axiom-4.
- Axiom 5
- 等腰三角形对称性
- 活动2：探索性质
- 全等三角形
- 三角形全等-SSA
- square root(平方根)
- 一元一次不等式圖形的副本
- 八年级下册
- Angles of a Right Triangle
- 矩形性质推论
- Trig Function Values (30 Degrees)
- Special Right Triangles 30-60-90
- Applying Pythagoras Theorem
- 5．勾股定理的证明
- Proof Without Words
- 勾股定理的几何原本证明
- 角平分线的性质的副本
- 正多边形外角和
- Interior angles of a Polygon
- Parallelogram: Area
- Properties of parallelogram
- Parallelograms (I)
- 中心对称的性质
- 中心对称图形
- 平行四边形到矩形
- Rectangle Area
- Exploring Rectangle
- 菱形有甚麼特性？
- Square Problem
- 平面直角坐标系
- 平面直角坐标系的构成
- Coordinate Points
- 1.6 Graphing Points in the Coordinate Plane
- 一次函数
- Graph the Line
- 九年级上册
- 反比例函数的图像
- k的几何意义
- 平行线分线段成比例
- 平行线分线段成比例定理
- 相似三角形
- 三角形の相似条件
- Summary of Conditions for Similarity of Triangles 相似三角形的判定條件：總結
- 相似三角形的性质
- 相似の位置
- 相似(相似比と相似の位置)
- 锐角三角函数
- 锐角三角函数
- Right Triangle Trigonometry: Intro
- 九年级下册
- 二次函数图像描点法
- 二次函数y=ax2+k图像描点法
- y=a(x-h)^2
- y=a(x-h)^2+k
- 二次函数配方法
- f(x)=a(x-d)(x-e)
- 圆的对称性
- 圆心角
- 圆周角与圆心角
- 圆周角定理
- 第24章-01 垂径定理-圆的对称轴
- 直线与圆相切
- 尺规作图_圆外一点做圆的切线(南京21年中考25题)
- 切线长定理
- 切线长定理
- Circle Theorems
- 弧长
- 圆的内接正多边形
- 圆锥侧面展开图
- 三角柱の投影図
- 三视图积木
- 三视图的副本
- 球体三视图
- 正方体堆垒三视图
- 正方体的三视图
Thermometer - Positive and Negative Numbers
Here are three situations involving changes in temperature. Represent each change on the applet, and draw it on a number line. Then, answer the questions.[br][br][list=1][*]At noon, the temperature was 5 degrees Celsius. By late afternoon, it has risen 6 degrees Celsius. What was the temperature late in the afternoon?[br][br][/*][*]The temperature was 8 degrees Celsius at midnight. By dawn, it has dropped 12 degrees Celsius. What was the temperature at dawn?[br][/*][/list]
Discuss with a partner!
How did you name the resulting temperature in each situation? Did both of you refer to each resulting temperature by the same name or different names?[br]
What does it mean when the resulting temperature is above 0 on the number line? What does it mean when a temperature is below 0?[br]
Do numbers below 0 make sense outside of the context of temperature? If you think so, give some examples to show how they make sense. If you don’t think so, give some examples to show otherwise.[br]
Linear Equations, Systems and Problems
1. Linear Equaitions
These equations are know as [b]linear[/b], because the [b]monomial literal part[/b] doesn't have an exponent (for example, [i]3x[/i] can be part of a linear equation, but [i]3x[sup]2[/sup][/i] can't because it's quadratic), so represented in a graph appear as a line. This fact assures us that if there is a solution, there can only be one solution (except in special cases were there are infinite solutions).[br][br]We say [i][b]if there is a solution[/b][/i] because sometimes equations don't have solutions. For example, the equation [i]x = x + 1[/i] (which means a number equals the consecutive number) doesn't have a solution, because this is never true. In reality, this equation is reduced to [i]1 = 0[/i], which is impossible.
Tips
[list][br][*]If we obtain an [b]impossible equality[/b], there is no solution, like [i]1 = 0[/i].[/*][/list][list][*]If we obtain an [b]equality that is always true[/b], whatever value gives a solution, then the solution is all real numbers. For example, if we obtain [i]0 = 0[/i].[br][/*][/list][list][*]When there are [b]denominators[/b] and we want to avoid them, we multiply the full equation by the same [b]least common multiple[/b] of the denominators. This way when we simplify, they disappear.[br][/*][/list][list][*][b]To remove the parenthesis[/b], we multiply the coefficient in front of it by all the elements it contains. This coefficient can be a negative sign (like –1, the content changes sign), a positive sign (like +1, the content doesn't change) or a positive or negative number or fractions (this number multiplies everything in the parentheses, changing the signs if its negative).[br][/*][/list][list][*]When we have a [b]nested parenthesis[/b], a parenthesis inside another parenthesis, we begging removing from outside to the inside. First, we remove the exterior parenthesis (multiplying it's content by the coefficients) and afterwards, we remove the rest the same way: from the most exterior to the interior.[br][/*][/list]
[b]Example 1[/b][br][br][img]https://www.matesfacil.com/ESO/Ecuaciones/Ecua1.jpg[/img][br]We add (or subtract) the monomials on the literal part (the [i]x[/i]'s with [i]x[/i]'s and numbers with numbers). What is adding on one side, will change to the other side subtracting and vice versa.[br]Afterwards, we put the [i]x[/i]'s to one side of the equality and the numbers to the other.[br][br][img]https://www.matesfacil.com/ESO/Ecuaciones/Ecua1-1.jpg[/img][br][br][b]Example 2[br][br][/b][b][img]https://www.matesfacil.com/ESO/Ecuaciones/Ecua3.jpg[/img][br][/b]First, we remove the parenthesis: because it has a negative sign in front of it, we chance the sign of all the elements in the inside.[br]Afterwards, all we need is to group the [i]x[/i]'s at one side and the numbers at the other.[br][br][img]https://www.matesfacil.com/ESO/Ecuaciones/Ecua1-3.jpg[/img][br]Because the [i]x[/i] has a coefficient, 2, that is multiplying, it moves to the other side dividing.[br][br][b]More examples:[br][/b][list][br][*][url=https://www.matesfacil.com/english/secondary/linear-equations-solved.html]Solved linear equations[/url][br][*][url=https://www.matesfacil.com/english/secondary/resolved-problems-linear-equations.html]Solved problems of linear equations[/url][br][/list]
2. Linear equation system
A [b]linear equation system[/b] is a group of equations (linear) that have more than one [b]unknown factor[/b]. The unknown factors appear in various equations, but doesn't need to be in all of them. What these equations do is relate all the unknown factors amongst themselves. For example:[br][br][img]https://www.matesfacil.com/ESO/Ecuaciones/SistEcua1.png[/img][br][br]We have basically thre methods for solving a system: [br][br][list][br][*][b]Substitution (elimination of variables):[/b] It consists in isolating one of the unknown factors (for example [i]x[/i]) and substitute that expression in the other equation. This way we obtain a first degree equation with the unknown factor [i]y[/i]. Once resolved, we obtain the value of [i]x[/i] using the value of [i]y[/i] we know.[br][/*][*][b]Addition, Reduction or row reduction:[/b] It consists in operating the equations, for example, adding or subtracting both equations so one of the unknown factors disappears. This way we obtain an equation with only one known factor.[br][/*][/list][list][*][b]Equalization:[/b] It consists in isolating from both equations the same unknown factor to be able to equal both expression, obtaining one equation with one unknown factor.[br][/*][/list][br][b]Example 1: substitution[br][/b][b][br][/b][b][img]https://www.matesfacil.com/ESO/Ecuaciones/SistEcua1.png[/img][br][/b][br]We isolate the [i]x[/i] from the first equation:[br][br][img]https://www.matesfacil.com/ESO/Ecuaciones/SistEcua1-1.png[/img][br]And we substitute it in the second:[br][br][img]https://www.matesfacil.com/ESO/Ecuaciones/SistEcua1-2.png[/img][br][br]We work out [i]x[/i] knowing [i]y[/i]:[br][br][img]https://www.matesfacil.com/ESO/Ecuaciones/SistEcua1-3.png[/img][br][br]Therefor, the solution to the system is[br][br][img]https://www.matesfacil.com/ESO/Ecuaciones/SistEcua1-4.png[/img][br][b]Example 2: addition[br][br][/b][b][img]https://www.matesfacil.com/ESO/Ecuaciones/SistEcua1.png[/img][br][/b][br]We multiply by –2 the first equation, we add the equations and resolve the equation we have obtained[br][br][img]https://www.matesfacil.com/ESO/Ecuaciones/SistEcua1-9.png[/img][br][br]We replace the value of [i]y[/i] in the first equation and we solve it:[br][br][img]https://www.matesfacil.com/ESO/Ecuaciones/SistEcua1-10.png[/img][br][br]Therefor, the solution to the system is[br][br][img]https://www.matesfacil.com/ESO/Ecuaciones/SistEcua1-11.png[/img][br][br][b]Example 3: equalization [br][br][/b][b][img]https://www.matesfacil.com/ESO/Ecuaciones/SistEcua1.png[/img][br][/b][br]We isolate [i]y[/i] from both equations:[br][br][img]https://www.matesfacil.com/ESO/Ecuaciones/SistEcua1-5.png[/img][br][br]We equal both expressions and we resolve the equation:[br][br][img]https://www.matesfacil.com/ESO/Ecuaciones/SistEcua1-6.png[/img][br][br]Substituting in the first of the previous equations,[br][br][img]https://www.matesfacil.com/ESO/Ecuaciones/SistEcua1-7.png[/img][br][br]Therefor, the solution to the system is[br][br][img]https://www.matesfacil.com/ESO/Ecuaciones/SistEcua1-8.png[/img][br][br][b]More examples:[br][/b][list][br][*][url=https://www.matesfacil.com/english/secondary/solving-linear-equation-systems.html]Solving a linear equation system[/url][br][br][*][url=https://www.matesfacil.com/english/secondary/resolved-problems-linear-equation-systems.html]Solved problems of linear equation systems[/url][br][/list]
[b]More information: [br][br][/b][list][br][*][url=https://www.matesfacil.com/english/high/solving-systems-by-Gaussian-Elimination.html]Gaussian Elimination (matrix algebra)[/url][br][br][*][url=https://www.matesfacil.com/english/]Index of math contents[/url][br][/list]
[right][/right][center][img]https://www.matesfacil.com/LOGOHOMEz.jpg[/img][br][b]Matesfacil.com by [url=https://www.matesfacil.com/]J. Llopis [/url]is licensed under a [url=http://creativecommons.org/licenses/by-nc/4.0/]Creative Commons Attribution-NonCommercial 4.0 International License[/url].[/b][/center]
三角形三边关系
Angles of a Right Triangle
[color=#000000]Interact with the applet below for a few minutes.[br]Then answer the questions that follow. [/color]
In the applet above, what is the measure of the gray angle? How do you know this?
What is the sum of the measures of the 2 acute angles of this triangle?
What vocabulary term (adjective, really) describes the relationship between the [color=#ff00ff][b]pink angle[/b][/color] and [color=#1e84cc][b]blue angle[/b][/color]?
Fill in the blanks with appropriate responses to make a true statement! [br][br]The 2 __________ angles of a ____________ triangle are ______________________!