A remarkable aspect of the Internet is that nothing ever goes away; the flipside of that, for any search you conduct, is the amazing number of pages returned that may bear only the most tenuous connection to what you are looking for.
Contrary to people’s idea that, for each query, search engines turn up exactly the answer you need, instead you get a mishmash of information that you then have to sift through to find what you want.
In defending the Internet, some aver that you only need to ask the right question. The trouble is: what is the right question?
Let’s say you need practice calculating the area and volume of 3D shapes or maybe gain a better understanding of congruent triangles, so you set out to find geometry worksheets.
Typing ‘geometry worksheets’ into your favourite web browser will indeed result in a list of worksheets; now you can study to your heart’s content.
Wait a minute! Are these indeed the aspects of geometry you need to study or did you get a bunch of random sheets that have no relation to the particular shape or structure you need help with?
That is why your Superprof has combed the Internet for the best geometry resources and organised them by their level and usage.
Now we turn this handy directory over to you… so you can do less searching and more geometry.
Grab your compass and straightedge; here we go!
General Geometry Resources
A rather remarkable aspect of the education system in the UK is that maths skills are not taught in a vacuum.
Students start learning geometry (and mathematics) from the earliest Key Stages and they continue to study geometry as they advance through each level, while the maths curriculum get progressively more complex – and, some would say, more difficult.
By contrast, math learners across the pond, in the US, don’t start learning higher math until a few years later in their academic career and, even then, each facet – trigonometry, geometry and algebra and taught as subjects onto themselves, with little connection given to the big picture: that all maths are related.
As a maths student in the UK (or the parent of such a maths student), you probably do not much care how Americans learn their math; you only want to find answers to your math questions.
We mention the difference between learning systems because many of the online resources for practising geometry and maths, in general, are American-born and are targeted to American students.
Still, these are fantastic sources of information and, if you can manage to overlook the differences in spelling and pronunciation (in the video presentations), there is a lode of geometry information to be mined.
ThoughtCo is a reference site whose content is written by professionals at the top of their fields in language that is easy to understand, whether you want to know more about biology, history or maths.
Their site is uncluttered and well-organised and, while on their pages, you won’t suffer annoying pop-ups that want to send you notifications or enticements to buy anything.
From their home page, it is easy to navigate to the math/science page and select geometry. There, you will find informational articles and printable worksheets to challenge your skills.
A single article lists the most important geometry definitions:
- line segment: a portion of a line that is between defined points
- ray: the segment of a line from a set point, and any points along that line
- angles: acute angles, right angles and obtuse angles, and what defines themselves
- they also feature straight angles, reflex angles and complementary/supplementary angles
- Euclidean geometry and postulates
- Intersecting lines, line midpoint and bisectors
In one fell swoop, ThoughtCo covers basic geometry; the rest of their pages on the subject cover more advanced concepts with accompanying worksheets you can print and work on.
With ThoughtCo, you can regale yourself with all of the basic geometry you need: equations, examples and worksheets. Our next website provides video instruction…
With Khan, the difference between the American education system and our is much more pronounced; all of their material is organised according to the US education system.
Khan affords you the option of searching for learning materials by ‘grade’ which roughly corresponds to our ‘year’ system. For instance, a British Year 10 student is roughly equivalent to an American 9th -grade student... but there are no firm, parallel lines between the levels, so you may have to hunt around a bit for exactly what you are looking for.
Another point to remember is that American math students generally do not encounter geometry until they are in secondary school so, if you select ‘geometry’ from the site’s homepage, you will be directed to ‘high school geometry’ - which may well be where you need to go.
Keep these points in mind as you search for geometry instruction on Khan!
Now that you’ve arrived at the ‘high school math’ page, you may start your instruction by going over the bases of geometry: angles and polygons, and calculating the areas of such.
Don’t forget to partake of their full overview of the Pythagorean theorem!
You may also choose to move on to the topic you need the most help with: congruence, similar triangles, trigonometric ratios…
Each segment is clearly marked; you can search for the topic that particularly interests you (or bedevils you!), watch the videos on that subject and then take an exam.
If you’d rather not create an account and launch yourself headlong into video instruction, you may read the review articles listed at the bottom of the maths/geometry page.
Both of these American sites provide fantastic resources to master the fundamentals of geometric figures, now let’s get a bit more international.
Massive Open Online Courses
If you are preparing to sit your GCSEs or A-Levels, you will probably need more advanced materials to study from/with.
The new wave in education, these MOOCs, may just be the thing that will get you ready to sit your school-leaving or university entrance exams.
As their name implies, they are conducted strictly online and they are open to anyone who has an interest. Some courses cost a small fee while others are completely free but for enrolment into the website or programme.
Many top-name schools often host such courses but combing those schools’ websites to find them might bring you more frustration and aggravation than it’s worth. The solution for that is… you guessed it: another website (or three)!
Coursera is one of the top names in MOOCs. They offer everything from free courses in AI and algorithms to a full degree course to earn an MBA. Their courses usually originate from top-named US schools.
Their curriculum is unfortunately not tailored to anyone needing an in-depth understanding of geometric constructions; theirs is more of a hit-and-miss proposition.
To wit, we searched their database for a geometry course and, while they had one listed, it was not currently active. Still, Coursera has plenty to offer; they are well worth bookmarking for later exploration.
FutureLearn works in much the same way as Coursera and also originates in the US. They are less inclined to offer courses at no cost.
If you are feeling adventurous, you may try MOOC List.
They compile and list MOOCs from any school, anywhere in the world. No need to worry; they let you know where the course originates from and which language it is taught in.
Remember, in the introduction to this article, that we said everything ever put into cyberspace is still there?
That also holds true for MOOC-list; some of their course listings show a start date of 2016! But then, some show an imminent start date too. Maybe they just haven’t gotten around to culling all of the outdated classes…
Have you considered finding a geometry tutor who will help you master Pythagorean triples and similar geometry problems?
Sites to Help you Learn Geometry
It’s quite nice that our American friends put so much geometrical information into cyberspace for all to learn from but we Brits have a few pages of our own to turn to.
Take, for instance, Teach It Primary.
Their geometry resources page is targeted to Key Stage 2 students so that they can better understand shapes: comparing and classifying them, their properties and how they are constructed.
If you feel the need to investigate a quadrilateral in depth, their exercises blending quadrilaterals and scissors are sure to be a hit. Conversely, if calculating the area of a circle or distinguishing the types of triangles stymies you, there, you would be well-served.
From the table below, you can find a summary of the geometry help - some that we’ve listed in this article; their web addresses and what you can find there.
List of Helpful Geometry Web Pages
|Site Name||Web Address||What You Will Find|
|Khan Academy||www.khanacademy.org||Instructional videos and worksheets organised by level (designed for US students!)|
|Thought Co.||www.thoughtco.com||Articles, worksheets and geometric formulas|
|Coursera||www.coursera.org||Open online learning courses pertaining to geometry or other geometry applications|
|FutureLearn||www.futurelearn.com||Geometry and geometry-related open courses (as available)|
|MOOC List||www.mooc-list.com||An assortment of MOOCs; a search will pull up all geometry-related courses|
|Teach It Primary||www.teachitprimary.co.uk||General math learning resources including a page for geometry|
|TTS Group||www.tts-group.co.uk||Shapes, puzzles and various geometry-related items for sale|
|Homeschool Math||www.homeschoolmath.net||Geometry lessons and worksheets; links to further geometry learning sites (designed for US students!)|
|Analyze Math||www.analyzemath.com||Abundant math resources including geometry formulae and worksheets|
Whether it is the humble triangle or the lofty-sounding parallelogram that is giving you fits; whether you want to deepen your trove of knowledge about geometric shapes in general or theorems in particular, you can turn to any of these pages for the information you need... without having to figure out the right question to ask your browser!
Don’t stop now! Discover our beginner’s guide to geometry...