Congruent Triangle

Congruent Triangle Congruent triangles are the triangles which have their respective corresponding sides and corresponding angles equal to each other. This implies that the corresponding sides of one triangle are equal to the corresponding sides of the other triangle. Similarly, corresponding angles of one triangle are equal to the corresponding angles of the other triangle, and then the two triangles are called as congruent triangles. Congruency between two triangles can be proved using congruency properties such as SAS, SSS, ASA, AAS and HL (only for right triangles). Example 1: In triangle ABC, angle ABC is 35, angle ACB is 75 and side BC = 5m. In triangle XYZ, angle XYZ is 35, angle XZY is 75 and side YZ is 5m. Are ABC and XYZ congruent triangles? According to ASA (Angle-included side-Angle congruency property), corresponding 2 angles and an included side are equal in both the triangles and hence they are congruent triangles. Example 2: In triangle ABC, side AB = 3m, side AC = 4m and angle BAC is 62. In triangle PQR, side PQ = 3m, PR= 4m and a ngle QPR is 62. Are ABC and PQR congruent triangles? According to SAS (Side-included Angle-Side congruency property), corresponding 2 sides and an included angle are equal in both the triangles and hence they are congruent triangles.

Online Statistics Tutoring Get Everything in a Click

Online Statistics Tutoring Get Everything in a Click Statistics is a subject that has a combination of mathematics, statistics and economics. The branches go hand in hand. It has a wide application in all the works. No matter what stream you choose, stats will be always complimentary! Data, raw figures, constants, the X’s and Y’s, styles of presentation of facts and pinch of economics is all that statistics consist of. Don’t be afraid, it’s not that tough as it seems. With the online statistical tutors  available, statistics becomes an easy to go subject. The online tutors are always present to teach you the basic concept of mathematical statistics. They engross you with various easy going methods and inculcate the base of statistics in the initial practices. The online statistical tutorial  consists of the polished ways to teach you the methods used for the representation of data. The tutor teaches you in an audio-visual mode along with the basic graphs and figures, without which statistics cannot be taught. Your screen will also consist of a portion where you can type your queries which will be resolved by the tutor then and there itself. Statistics tutors covers following topics: The average Variance of a population Standard deviation Mean, mode and median Probability and statistics Sample variance The best part of online tutorial is the two-way communication that is possible between you and your teacher. Plus the experienced tutors teach you in an easy way that can be understood even by a fresher. So don’t wait, register yourself with the online masters and make the best of your time!    

Top Tips for Budding Pianists

Top Tips for Budding Pianists How Do You Become a Pianist? Chapters When Should I Practice Playing the Piano? How Can I Improve My Dexterity? How Can You Learn to Play the Piano and Sing at the Same Time? How Can You Simplify a Piano Piece? How Do You Compose a Piano Piece?It's not easy when you learn piano. Even before you start, you have to be motivated and ready to put your heart and soul into it. Even with the help of a piano teacher, learning how to play piano is a long and hard process.You need to study regularly in order to become a piano player and even then you need to keep practicing to make sure you never forget it. Don’t get discouraged or skip any of the steps. Learning music is unforgiving.You need to learn how to read music and then study music theory. After that you need to work on your dexterity and using your hands independently of one another. Reading sheet music like a book, improvising, and playing and singing at the same time are all things that come after years of practicing.Here’s some advice your becoming a piani st and playing the piano well. LouisPiano Teacher £40/h1st lesson free!Discover all our tutors AlisonPiano Teacher £32/h1st lesson free!Discover all our tutors ErenPiano Teacher 5.00 (6) £40/h1st lesson free!Discover all our tutors BarbaraPiano Teacher £50/h1st lesson free!Discover all our tutors Chi yuenPiano Teacher 5.00 (5) £30/h1st lesson free!Discover all our tutors TomPiano Teacher £25/h1st lesson free!Discover all our tutors ValtiePiano Teacher £35/h1st lesson free!Discover all our tutors DanielPiano Teacher 5.00 (5) £37/h1st lesson free!Discover all our tutors When Should I Practice Playing the Piano?In order to progress with your learning, there’s a few things you’ll need:free timemotivationwillingnessdisciplinea good earYou should practice at least 30 minutes each day. (Source: Crazy Banana)A tutor will provide their student with a method to help them progress during a lesson. However, they can't constantly look over their student’s shoulder outside of cla ss. This means that the student needs to practice on their own.How often should a student work individually on their piano exercises?It takes regular practice to learn how to play the piano: playing for three hours once in a while or just before your lessons isn’t enough to improve and will probably render your lessons ineffective. You need to focus and memorize things.You could say that you should practice the piano whenever you want. This might sound a bit like a cliché but you should play whenever you feel like playing. Just make sure when you do that it’s effective practice and not just messing around.Doing two hours of practice before your tutorials is a quick way to slow down your progress. It’s essential to put aside some time every day to practice playing the piano. At least half an hour a day should be enough. Making sure that you practice a certain piece means that you’ll have to stop doing whatever you were doing instead.What if you can’t read the piece from yo ur last piano lesson? Have a look on-line for tutorials. There are plenty of free piano lessons on-line and video tutorials that could help. A quick on-line search should get you the results you're looking for.However, if you’re genuinely motivated and want to learn, you won’t feel like you’re giving up any time at all.  We recommend thirty minutes of practice after dinner before you turn on the TV. This is when you tend to be at your most creative.However, there’s no one-size-fits-all solution. Everyone learns differently. You need to find the routine that works for you. Some people learn more quickly than others.  Some people may learn something in an hour while others may need four hours. It completely depends on your motivation.However, there are some things than anyone wanting to become a pianist should know:Practice should always be enjoyable.You need to focus and activate your memory in order for any learning to be effective.The more you practice, the more your finger s will separate and the easier you’ll find playing across several octaves. You’ll gain more and more dexterity. How Can I Improve My Dexterity?Improving their dexterity really annoys a number pianists. However, your private tutor can help you work on this.When we say dexterity, we're talking about your ability to quickly and accurately navigate the keyboard with your hands, especially when the notes are fairly far apart.Dexterity can improve how well you hit your piano targets. (Source: Wikimedia Commons)When you first start, your hands will probably be fairly stiff. The quickest way to improve your dexterity is to practice:do exercises going up and down octaves.learn to go from one chord to another quickly and fluidly.do exercises to improve your finger span: flex your fingers.play scales on the piano: start slowly and then get faster and fasterwork on common chord progressionsget used to not looking at your fingers when you’re playing.You’ll soon start to make more and mor e progress. These exercises will be hugely beneficial in the long-term, especially if you’d like to one day be able to sing and play at the same time, compose your own music, and become a skilled and well-rounded pianist in the process.Once you feel comfortable playing your scales at relatively quick speed, start working on your coordination by playing sections with your left hand, then your right, and finally combing the two together. First slowly, then more quickly.You should always practice your scales just before your lessons. First C major, then D major, etc. It’s good for warming up your fingers and mentally preparing your ear for music. Having a good knowledge of your scales is also great for improvising with other musicians.A budding musician should master their scales in order to learn as quickly and as effectively as possible. Use piano methods:  Hanon and Czerny exercises are great for warming up your fingers and getting better and putting chords together.In order to improve your dexterity, you should regularly do these exercises. This will help you to play with precision and train your fingers to play the piano better. Every good pianist should be able to play chords and arpeggios precisely.What’s the next step? Learning to play and sing at the same time. LouisPiano Teacher £40/h1st lesson free!Discover all our tutors AlisonPiano Teacher £32/h1st lesson free!Discover all our tutors ErenPiano Teacher 5.00 (6) £40/h1st lesson free!Discover all our tutors BarbaraPiano Teacher £50/h1st lesson free!Discover all our tutors Chi yuenPiano Teacher 5.00 (5) £30/h1st lesson free!Discover all our tutors TomPiano Teacher £25/h1st lesson free!Discover all our tutors ValtiePiano Teacher £35/h1st lesson free!Discover all our tutors DanielPiano Teacher 5.00 (5) £37/h1st lesson free!Discover all our tutors How Can You Learn to Play the Piano and Sing at the Same Time?Singing while playing piano is tricky. It’s basically playing two instruments at the same time and it's not easy.Singing and playing at the same time may be difficult but it's not impossible. (Source: PeakPX)Even a privately taught pianist can forget everything when they have to start singing.To sing and play at the same time, you have to first master the piano part, then the singing part, then bring the two parts together.  When bringing the two parts together, you need to both coordinate your two hands then synchronize them with your voice.In the same way you coordinate your two hands when learning to play the piano, you’ll have to repeat the same process in order to sing while you play. It’s recommended that you start with a fairly simple song with a simple chord progression and no vocal gymnastics.  Choose a song in common time (4/4) in C-major, for example.You should also try playing the song while humming before you try singing along. This allows you to focus on the vocal melody and the piano part. This means you won’t get distracted by trying to rem ember the lyrics.If you really want to learn to sing and play piano at the same time, you need to learn your source material inside out. You need to know every vocal nuance by heart.To summarize, here are the key points for singing and playing piano at the same time:Be patient, determined, and persevering.Adopt a good posture for playing and singing.Play the piano part and practice the singing part separately.Choose a simple song.Play the song while speaking (to see if you know it well enough).Listen to the original song a lot.Break down the lyrics into syllables.Use a metronome or tap your foot to keep time.More complex songs require more work. Perhaps you need to simplify the music itself.Your private tutor should be able to help you with simplifying the piece.Has your search for piano lessons London yielded satisfactory results? Why not check out Superprof's piano teachers, now! How Can You Simplify a Piano Piece?It might be beneficial to simplify the piece in order to make it mo re playable on the piano.Being able to simplify piano music is one of your most important tools. (Source: Tanner Randall)Some songs are incredibly complex, unreadable, or contain substitutions (which are very common in jazz).Simplifying a song by making it more playable on the piano is sometimes necessary if the person playing the piece doesn’t have the necessary level to play the song in all its complexity. This is much better than discouraging the pianist.It’s also a good idea to listen to the song plenty of times before trying to simplify it.  Make a note of the chords as you listen and play them on the piano. This practice will help you get to know the song much better than just listening to it.Identify the chords, then practice the chord progression, starting off slowly and getting faster and faster until you’re playing at the same tempo as the song. You have to work out the main chords in order to pick apart a song.Finding the root note of each chord is essential when it comes to analyzing a song.  The pianist can then work out the chord’s harmonies and whether the chord is a major chord, minor chord, a fifth, seventh, etc.  You need to be familiar with music theory in order to do this.If you’ve been working on your dexterity, you should be able to put these chord progressions together yourself. How Do You Compose a Piano Piece?Here’s some advice for composing a piece for piano: Know your music theory and think creatively.To become a composer, you need to be inspired. (Source: pxhere)Have a good technical ability: you can’t compose as a beginner.  You need to know how to put chords together, their inversions, common rhythms, etc.You also need to have a good knowledge of music, different genres and styles, etc.  Be familiar with reading sheet music: reading sheet music like you would a book.  You need to encourage imagination and creativity in order to compose a piece on piano. It’s difficult but also very rewarding.Use a metronome to impr ove your rhythm. It might be annoying to listen to but it’ll ensure that you’re always in time. Make sure you know your time signatures. Is this going to be a waltz or a march?Choose the right chords to work with the feel of your piece. Remember that minor chords tend to give a piece a melancholic feel. On the other hand, major chords feel optimistic and happy. You also need to think about the lyrics. Make sure the chords go well together: certain progression evoke certain feelings.Once you’ve considered all this, you need to work out how you’re going to play it.You can use the chords to focus on the the song’s rhythmic qualities. What about deconstructing the chords and playing them as arpeggios to give the song a more melodic quality.Don’t forget to record your creations!  Sometimes you’ll come up with nothing. However, sometimes you’ll stumble upon something amazing. You’d hate to forget what it was, right?  With a microphone and a music program, you can start p utting your ideas together and working on them.  It’s always a good idea to record yourself when you’re improvising.  Then you can listen back to it and write down what you did. Make sure your theory’s good.Becoming a pianist is basically and long and difficult journey. However, this is what’s so beautiful about the piano. It’ll be worth it in the end!

A Birds Eye View English Listening Exercise

A Birds Eye View English Listening Exercise When speaking English, as in most languages, we typically use directions like up, down, left and right to describe directions. But imagine if you spoke a language that didnt use these directions. Imagine telling someone to raise their northwest hand, or go north down the hallway, and enter the first door on the east. Pigeons know their way around.There are several languages that do rely on a strong sense of direction to speak the language. In this English listening exercise, youll hear a podcast about how pigeons and humans can have an amazing sense of direction, when they pay attention and use their birds eye view. You can find and download the podcast here, or play it below. Contact us if youd like to take a class using this listening exercise. /* */ What was unusual about the war hero that Mindy talked about?Why pigeons?A.B.What was the problem for the British?What was so amazing about what GI Joe did?If you go ___ ___ __ ____ to the center of the earth, theres ___ ____ metal __ __ _____, churning.You long to grab one by the ____ ___ ___ ____ and ask them how they do this.What dont some languages have?How do you say hello in the Australian aboriginal language?How do they always know their direction, even indoors, according to the scientist?What did she see in her mind after a week in Austrailia?What is a birds-eye view?What interesting thing did Karen Jacobsen do?

Choosing the Right SAT Subject Tests

Choosing the Right SAT Subject Tests During the test preparation process, the sheer number of tests and test dates can be overwhelming. Here at AJ, we have an expert knowledge of college entrance exams and can help you navigate the journey. Here’s a brief guide to one test (the SAT Subject Test, or SAT II) and how students can choose the right ones for them.OverviewUnlike the SAT, which is broad and covers many skills and content areas, the SAT Subject Tests focus on specific subjects taught in school. Because students are already preparing for finals at the end of the junior year, May and June are ideal months to take the SAT Subject tests. Acing the SAT Subject tests is a great way to show what you’ve learned throughout the year.There are 20 SAT Subject Tests, each of which is an hour in length, scored from 200-800, and comprised entirely of multiple choice questions. You can take up to 3 tests per test date, but we often find that 1-2 is ideal due to potential test day exhaustion.Factors to Consider in Choosing a TestYou can see a complete list of SAT Subject Test offerings here. The best way to see which SAT Subject tests are right for you is to take practice tests and score them. Here are a couple of key guidelines that can help along the way.1. College GoalsAdmission requirements around SAT Subject Tests vary widely among colleges. Many elites schools require or recommend 2-3 SAT Subject Tests. Examples include Brown University, Georgetown University, Caltech, Rice University, and Tufts University. You can find specific requirements on every school’s website, so it’s a valuable exercise to sit down and make a list of what your student will need to include in the application. If even a couple of your student’s top choices require or recommend SAT Subject Tests, it will be wise to have him or her pick exams and schedule a test date.2. The Student’s Strengths and CourseworkAP courses often translate well to the SAT Subject Tests, so if, for example, a student is excelling in AP Biol ogy and AP English Language Literature during her junior year, the SAT Biology and SAT Literature should be strong contenders for a May or June test date. Keep in mind that, while the AP’s and SAT’s often have much content overlap, there are certainly differences, and the formats are quite different. AP Exams rely more on essays and long-form responses as opposed to the strict multiple-choice format of the SAT’s. Thus, it’s important to be strategic and plan on preparing for both the AP and SAT separately towards the end of the course.3. CoachabilityIn addition to any solid AP coursework or obvious subject test affinities, we find that the Math II and Literature exams are great choices for many students. A junior who has taken or is taking pre-calculus will have completed all necessary coursework for both exams. Furthermore, these exams are especially coachable and strategic in nature, and our students have historically seen a great deal of success and improvement on these exams. For example: while we have an excellent record of success with all of the subjects, our biggest score increases come from the Math Level 2 SAT Subject Test, with many students improving over 100 points.How to Prepare for the TestsAJ Tutoring knows the SAT Subject Tests with a degree of expertise bordering on obsession. Luckily for students, a minimalistic approach focusing on a few key test-taking strategies, a series of full-length practice exams, and a targeted content review can work wonders in maximizing performance on test day.Our SAT Subject Test Students typically complete 3-4 sessions of 1.5 hours each. They start with an hour-long practice exam which serves as a jumping off point for a highly customized preparation beginning with session #1. In a 1-on-1 format, the tutor will observe the student’s strengths and weaknesses and tailor the instruction to fit his or her needs, assigning practice, reviewing gaps, and coaching on question evaluation as they go.You can le arn more about our preparation process here.Please reach out to us today to make a test prep plan for your student!

How to Learn (or Relearn) Maths as an Adult

How to Learn (or Relearn) Maths as an Adult There are many reasons you may want to learn maths again as an adult. Perhaps, you want to help your children with their schoolwork, refresh your knowledge in general or even sit your GCSE or A-Level as an adult. Whatever your reasons, here's what you need to do. Think about your maths mindset Many adult learners have a fear about maths, feeling that they can't do it, and they will struggle if they try again. This fear comes from past experiences at home and in school, and if you don't tackle it - it can be detrimental to your decision to study maths again. Alongside this are lots of negative attitudes towards maths in general. Maybe you don't believe you have a mathematical brain. Or perhaps you feel that because you find maths hard, you can never be good at it. None of this is true. So, the first thing to do before you start again is to change your maths mindset. Step one is to forget what happened when you were at school and what was said about your mathematical ability. Step two is then to find yourself the right teacher/tutor. The right person for you will motivate you, explain mathematical theories in a way you can understand and capture your interest with maths. How will you go about learning maths? There are several ways to target maths. 1. You can do it yourself you with books, past papers and with excellent websites like BBC Bitesize Maths and tutorials on YouTube. 2. You can apply for a maths course at a beginner or GCSE level as an adult learner at a local college. 3. You can find a maths tutor. The right tutor will be able to talk you through what you need to learn, how to learn it and also tailor it to where you are right now. We have maths tutors for the casual learner and maths tutors for advanced level learners. Consider where you need to start What you need to address, depends on how much maths knowledge and confidence you have right now. If you are a complete beginner, then courses and tutors can help you start from the beginning. If you haven't studied maths since you were at school, colleges and tutors can also refresh and extend your maths skills to help you gain a formal qualification. If you are keen to take or retake maths GCSE, then check out our blog on How to Pass Maths GCSE As this highlights the mathematical basics you need to know at this level: (1) Number - fractions decimals, percentages(2) Algebra - quadratic equations, factorising, indices(3) Ratio, proportion and rates of change - compound measures, measurements(4) Geometry and measures - angle theorems, 3 D shapes, vectors(5) Trigonometry - Pythagoras theorem, congruency(6) Statistics and probability - averages, data, sampling For A-Level and a maths degree, you will need to know more advanced maths theory and are better off working via a college, or with a maths tutor.

Tattoos Taboo or trendy

Tattoos Taboo or trendy My tattoos; love on the inside of my left wrist, and the crown from the Keep Calm and Carry On posters with KBO (a Winston Churchill catchphrase which stands for keep buggering on) underneath it on the inside of my right ankle. Photo taken by me. Im 28 years old, I have a BA in History and am a semester and a third away from a BA in Communications, Ive never been arrested, never done drugs, and whilst I dont get to Mass every week, I go more often than Christmas/Easter/Holy Days. I also have two tattoos. Tattoos, I might add, that werent just drunken whims. And its not just me a number of my friends have at least one tattoo, and many of those have more than one. It seems like after every semester break, at least a couple people I know at school return sporting new ink. Naturally, this got me thinking about tattoos and how society in general feels about them. So of course I did a little research. In 2009, Pew Research did an end-of-decade survey asking the American public a series of questions about the previous ten years. One of the questions asked pointed out that more people were getting tattoos than in previous decades and asked respondents how they felt about that change. Just 7% said it was a change for the better whilst 45% said the change made no difference and 40% said it was a change for the worse. Earlier that year, CBS News posted a story entitled Tattoos Becoming More Accepted at Work, which cited the statistic that 23% of college students have one to three tattoos and that 36% over a third of adults aged 18 to 29 have them. In 2010, UK newspaper The Guardian reported that a survey indicated that one-fifth of British adults are inked. Another Pew Research study, this one conducted in 2010, aimed to create a portrait of the so-called Millennials generation (those aged 18-29 in 2010). The study puts the percentage of Millennials with tattoos at 38%. By comparison, the study says that 32% of Americans aged 30-45 have at least one tattoo, and then the numbers begin to drop away sharply: of Boomers (aged 46-64), 15% have at least one tattoo, and of those above age 65, just 6% sport ink. Whilst the stigma against tattoos/tattooed individuals appears to be going strong amongst older Americans, amongst those 45 and under there is an increasing tolerance of and even enthusiasm for tattoos. This has significant implications as far as workplace policies regarding tattoos are concerned; if society in general is more accepting of tattoos, it follows that visible tattoos will become less of an issue. That being said, a full 70% of Millennials and 73% of those aged 30 or older said that their tattoos are normally not visible. Early this year, Harris Interactive conducted a new poll regarding tattoos. According to the poll, 21% of U.S. adults report having a tattoo, which is up from previous years. It seems that with the increasing number of adults with tattoos this permanent body art is becoming more accepted fewer people think it is related to deviant behavior than before yet among those without tattoos there are still several negative stigmas associated with having tattoos. All in all, each later poll seems to show an increasing amount of acceptance, or at least ambivalence as opposed to negative reactions, towards tattoos and individuals who have them. Additionally, all of the polls that ask people with tattoos if they regret getting them, a large majority (as high as 84%) said that they do not. It seems, then, that tattoos might still be taboo with older generations, but they are increasingly trendy amongst younger generations, especially college-aged individuals. If you are considering getting a tattoo, I have a few pieces of advice. Plan what you want, where on your body you want it, and where in the world youre going to get it beforehand. Do your research, especially about tattoo shops and artists in your area. You want to find somewhere that is clean, safe, and friendly. And if youre going to have their work on your body for the rest of your life, you want your tattoo artist to be someone whose work you admire. Dont get tattooed when you are drunk, and if youre getting tattoo number one its probably a good idea not to do it on a whim. Most importantly, though, do everything you can to make sure that youll be in that 84% of tattooed individuals who dont have any tattoos they regret.