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Triangles
Isosceles
Isosceles is when two sides of a triangle are the same length. To remember this term, you can notice the -sos is the word Isosceles. The s stands for the two sides, which will remind you that an isosceles triangle is a triangle with two equal sides.
Equilateral
Equilateral triangles are when all sides of a triangle are the same length. We can remember this by using the prefix -equal, which can stand for equality. Because the word equal is in the word, we can use this to recognize that an equilateral triangle is a triangle with all the sides in equal length.
Scalene
With isosceles and equilateral triangles being the first two, it leaves us with scalene. Scalene triangles are when all three sides are of different lengths. We can already infer this since there are no more possible combinations of possibility. (Either all sides are equal, different, or two sides are the same.)
Angles
Acute
An acute angle is an angle that is less than 90 degrees. A 90-degree angle is an angle that stands straight up from a horizontal line. If the angle is measured lower than 90 degrees, then it is called an acute angle. We can also tell if it is an acute angle by the way it looks. If it is slanted toward the right more than it is upright, then it is going to be acute.
Obtuse
An obtuse angle is an angle that is greater than 90 degrees, but less than 180. An angle of 180 degrees forms a straight line, so a straight line cannot be obtuse. So since an obtuse angle can be greater than 90 degrees but less than 180, possible measurements for the angle could be: 91 degrees, 100 degrees, 179 degrees, and 80 degrees. When there is an obtuse angle in a triangle, there can only be one angle that is greater than 90.
Right
A right angle is an angle that is exactly 90 degrees, not bigger or smaller than 90 degrees, exactly 90. Usually, there is a small cube on the angle to indicate that it is 90 degrees as seen here.
Straight Angle
Like mentioned before, a straight angle is an angle that measures 180 degrees. This forms a straight angle, like its name.
Reflex Angle
A reflex angle is the angle around an angle. It has to be more than 180, but less than 380 degrees. Here is a picture for you to understand.
Supplementary
Supplementary angles are angles that add up to 180 degrees. Remember, 180 is a line. To remember what a supplementary angle is, you notice that there is an s in the beginning of the word. The s can stand for the s in straight, which can represent a straight line. the straight line is 180 degrees, so supplementary angles will add up to 180 degrees.
Complementary
Complementary angles are angles that add up to 90 degrees. To remember what a complementary angle is, you can use the first letter of the word, c, and turn it into a 9 with a line. In case you are confused, here is a picture to showcase this trick.
Vertical Angles
Vertical Angles are angles that are vertical (or opposite) of each other and have the same angle. They are made by intersecting lines. For example, if we cut a circle into quarters, (four parts), then we would have four 90 degree angles. The first piece of the circle in the picture shown below has the same angle as the fourth angle. Both of them have an angle of 90 degrees. This is called a vertical angle. When solving questions like these, make sure to calculate the other angles of the lines and intersections as well, for sometimes angles appear to be vertical when being unequal.
Shapes
Congruent Figures
Two shapes are congruent if they share the same size and shape. Their angles and sides are equal to the other as well. To illustrate this, here is a picture of two congruent figures. However, the shape can be translated, rotated, and reflected, which I will talk about on the following paragraph.
Translation
When a shape is translated, it is moved. Not reshaped, rotated, or anything else, just moved. Each of the points of the shape must be moved the same distance and direction. If each corner of a shape is moved 5 spaces, then it is a translated. But if the shape is inverted in the process, then it is not a translated shape. When you take the original shape and the translated shape, you will get congruent figures because the size, angles, sides, and shape did not change.
Rotation
Rotation is the turning of a shape. The size, angle, sides, and shape cannot be changed, but as long as it is rotated and nothing else, then it is going to be congruent to the original shape. To tell whether not or not a shape qualifies as a rotational shape, you can visualize the distance from the original center of the shape and compare it to the “rotational” shape. If the distance is the same, then the shape is a rotated shape and is congruent.
Reflection
Reflection is the inverted filter of a shape. This means that the shape is almost flipped in a way. This means a reflected upright figure will be upside down. The points from the two congruent shapes must be the same distance from the central line. The central line is the line that separates the two shapes. To make this simpler, here is a picture for you to understand better. The mirror line can be in any direction, left, right, upside down, and mostly common: straight.
Notes: Translation, Rotation, and Reflection are all examples of transformations, which is what we call these three congruent changes of shapes.
Numbers
Integers
Integers are whole numbers. They can be positive, negative, or zero. They cannot be decimals or fractions. Examples of integers are: 1, 0 33, 5,900 Non-examples of integers are: 3.14159…., -5.9, 10/9.
Prime Numbers
Prime numbers are numbers that can only be divided by themselves and one. So, it will have only two divisors. This means that 1 is not a prime number, since it can only be divided by one multiple: itself. 0 is not a prime number either. Examples of prime numbers are 2, 3, 5, 7, 9, 11. Non-examples of prime numbers: 4 (can be divided by 2, 1, and 4), and 8 (can be divided by 1,2, 4, and 8)
Irrational Numbers
Irrational numbers are numbers that cannot be written as a ratio or fraction. This means they never stop. You have heard of pi, which is the number 3.14159265358979323….. The digits are ongoing. Fractions aren’t irrational because fractions are basically ratios, which breaks the meaning of irrational numbers. When an irrational number times a rational number is multiplied, it will be a irrational number. This is the same if you multiply a irrational number times a irrational number: you would get an irrational number as well.
Rational Numbers
Rational numbers are numbers that can be made by two integers. This also means that rational numbers can be written as a fraction. For example, 1.5 can be written as 1 5/10 or 1 1/2, which makes it a rational number, not an irrational number, which cannot be written as a fraction. Examples of rational numbers are 3.5, 6.908, 12.56, 5, and 1/9. Examples of irrational numbers are: the square root of 2 and pi (3.14159…)
IMPORTANT: The bottom of rational number’s fraction cannot be 0.
孝子
ノルウェーの皇太子妃殿下=メッテ・マリットで検索すると
分かります。挫折から立ち直った素晴らしい女性です。
また、フジコ・ヘミングも、今は超有名な国際的ピアニストです。
彼女は、68歳までとても無名で、さらに不遇でした。
彼女が、もし若い時から有名なピアニストだったら、
人を感動させる弾き方は、できなかったと思います。
それから、近所の女の人は、あやさんと言います。
彼女は、今立派な看護師として働いています。
看護師は国家資格です。日本ではこの資格があれば、
年齢に関係なく80歳でも働けます。健康であればですが。
日本語で書いても翻訳すると、微妙に違ってきます。
英語は、常に主語を書く必要があります。
翻訳機能のことが、だんだんに理解できました。
失敗や挫折のない人生を送る人など、一人もいないと思います。
人には、何回転んでも必ず起き上がる逞しさが必要です。
孝子
夢を3つも持っていることは、とてもすばらしいことです。
夢を持つということが、それ自体とても重要です。
その夢が、叶うかどうかは、その次の問題です。
一生懸命に頑張っていれば、道は開けると思います。
あなたは、たぶん10代でしょう?
私の近所の女性は、小さい子供2人を抱え、40歳を過ぎてから
看護師の養成学校へ入学しました。3年間通学し、昨年3月卒業しました。
看護師の試験にも合格し、今元気に働いています。
また、日本にフジコ・ヘミングというピアニストがいます。今88歳で、彼女が演奏する
「ラ・カンパネラ」という曲は特に有名です。人の心を打つ、何かがあります。
フジコさんが、ピアニストとして有名になったのは、67歳の時でした。
それは、あまりに不遇な人生であったため、テレビで放映されたからです。
そこから、有名になり、逆転人生を歩みます。今は、世界各国でピアノの演奏会を
行っています。
また、ノルウェー皇太子の奥さん・メッテ マリットさん(今47歳)は、
若い時、非行少女で麻薬に溺れ、麻薬常習者の男性と付き合い、男の子を出産します。
シングルマザーとなりますが、子供を育てながら大学に入学し、皇太子と知り合いました。
そして、結婚に猛反対するノルウェー国民に向かって、過去の過ちを謝罪し、「今後は
正しい道を歩いていく」ということをテレビで放映しました。私はその放送を見て、誠実な彼女の姿に感動した記憶があります。
若いあなたに、「どのようなコメントを書けばいいのか」と何日も
考えていました。他の人と同じ速さで歩く必要もありません。
他の人と自分を比べる必要もありません。あなたはあなたで良いのです。
悩んだり失敗したり、努力しても報われないと思ったりしても、泣かないでください。
それらは、決して無駄にはなりません。がんばったことは、あなたの頭の中に、良い財産として残るからです。何かで成功するかもしれません。くじけなければ。
生きて行くということは、そういうことなのです。
私は、もう少しで70歳になります。
子供の頃、あまり目立たなかった子が、大人になったら見違えるように、
立派になった人をたくさん知っていますから。
Shannon Yan
What a great story! Thank you for sharing your encouraging words. I will try not to compare myself to others and work my hardest!
孝子
数学が分からなくても全く心配ありません。
普通に生活するために大切なことは、もっと他にあります。
あいさつをきちんとすること。人の話を注意して聞くこと等です。
大人になった時に、何の職業に就くかを想像してみましょう。
例えば美容師、花や、ケーキを作る職人、ウェイトレス等
世の中にたくさんの職業があります。この数学が分からなくても
できる仕事はたくさんありますから安心して下さい。
UNKNOWN
Unless I dream of being a robotic engineer, designer, and programmer.
孝子
可愛かったシャノンちゃんは、シャノン博士になってしまった。
幼かったシャノンちゃんが懐かしい。😂
孝子
この数学を楽しく理解できる人は、将来科学者になるでしょう。😊
Shannon Yan
Heh 😊