Geometry is a vast subject and also compulsory in high school. So, there’s no way around it. You have to make friends with it and the sooner you do it, the better. Apart from being vast, geometry is also quite interesting. A good score in this subject is a matter of your interest. Once you start loving this subject, A grades are guaranteed on the assessments.

Let’s talk about some surprising and must-know geometry concepts related to different shapes. This list will amaze you.

Geometry is Very Old

This is not a concept but a fact. Geometry is very old, older than many civilizations that we know about today. The earliest recorded evidence about geometry comes from Mesopotamia and Egypt where it was written and recorded in approximately 2 millennium BC. It was known to people in Indus Valley and it was obviously known to the Egyptians and Greeks.

Geometry was used for constructing pyramids and other buildings, land surveys, astronomy, sculpting, and much more. So, now that we know that Geometry has been around forever and is going to stay forever, why not dive nose-first into it and learn some interesting concepts?

Circle Concepts

1. A circle has the shortest perimeter among all the shapes of the same area.
2. The area inside the boundaries of the circle is known as Disc.
3. If you inscribe a circle inside a square, the diameter of the circle is equal to the side of the square.
4. An angle inside a semi-circle will always be a right angle.
5. A circle is the most symmetric shape because every line through its center is a line of reflection symmetry.

Triangle Concepts

1. A triangle is a polygon with the least number of sides.
2. A triangle can always be split into two right triangles.
3. The length of one side of a triangle is always shorter than the sum of the other two sides.
4. Any polygon can be divided into multiple triangles.
5. Triangles are used in construction for their extraordinary strength.

Square Concepts

1. A square is a rectangle with equal sides, a rhombus with right angles, and also a regular quadrilateral.
2. A square has a larger area as compared to all the other quadrilaterals with the same perimeter.
3. A square has 4 lines of reflectional symmetry.
4. A cube has 6 square faces and is like a square in three dimensions.
5. A square is an important shape in town planning.

Rectangle Concepts

1. All rectangles are parallelograms but all parallelograms are not rectangles.
2. When length (l) and breadth (b) are equal that means the rectangle is also a square.
3. The diagonals of the rectangle divide it into 4 triangles.
4. Rectangular shapes are more commonly found in the real world as compared to other shapes.
5. When a rectangle is moved through space, you get a solid structure which is known as a rectangular prism.

In the End

We hope you found some new information about the common shapes in this blog. We had a good time writing this one and hope you enjoyed it too. You can use the information presented here to show off your geometry knowledge. Spread the word, and share the concepts. 

Learn geometry concepts from our expert tutors. They will guide you in tackling geometry concepts easily. 

Ever wonder why some students just seem to have a knack for excelling in math while others don’t? Why do some students score great marks in math without too much effort?

Make the best of a math tutor or e tutoring? Pretty simple. They understand the language of math.

As a high school math tutor, one of my main objectives is to familiarize my students with the language of math. Yes, it is a language.

In fact, many English words and phrases can be directly translated into math symbols and operations. Learning this is like getting a math tutor free for good! Some  examples are:

1. of = multiply
2. percent = divide by 100
3. ratio comparison = division
4. difference = subtraction
5. product = multiplication
6. quotient = divide
7. increased by, more than = addition

Watching young children learn has convinced me that the best way to pick up a language is by regular practice. If children spend enough time in a situation where they absolutely must learn a new language, they learn it really quickly and effortlessly.

It’s the same with math. Students are faced with a barrage of intimidating terms as the list of topics is given to them during our summer math e-tutoring programs at eTutorWorld.

They are actually encouraged to use these terms without apprehension during their tutoring classes. A pictorial lesson then creates the visual memory aid and reinforces the idea. Once they are familiar with the language of math, they find the rest of the course a lot easier. Additionally, they are much, much more confident doing math.

Understand the Language of Math

Learning math effectively begins at an early age. There are a bunch of basics that, once taught, stay with the child throughout the school years. Whether you are a high school math tutor (face to face or via e-tutoring) or an elementary school teacher, getting your students familiar with the math language eases teaching as well. For instance, a Grade 3-4 child will need to be familiar with:

1. Multiplication and division strategies: Word examples, rather than just plain direct problems are a far more effective method of teaching these topics. Also, pictorially, arrays are a great tool to further reinforce this concept.
2. Fractions: Using the phrases ‘part and whole’ and ‘out of” go a long way in familiarizing the child with fractions. Using ‘building blocks ‘ as an analogy further strengthens this idea.
3. Ratios: There are 2 concepts in ratios.

(a) One ratio as part of another: This is an extension of equivalent fractions and can be beautifully illustrated by ‘dividing rectangles’. For instance, “ Three out of four parts and six out of eight parts” mean the same thing. Explaining that the denominator is “the total number of parts” and the numerator is “the number of selected parts” helps a great deal.

(b) Sharing ratios: Once the child learns the idea of ratios as illustrated above, the idea of sharing ratios becomes simpler. For instance, if $48 is divided into 2:3:7 between 3 people and you need to find how much money each person gets, use the following steps (and the terms, of course!)

• Adding up all the ratios gives you the ratio sum(2+3+7=12).
• Dividing the whole by the ratio sum(48/12) gives you the multiplier (4).
• Multiplying this by each number gives you the respective shares,

($2 x 4 = $8, $3 x 4 = $12, $7 x 4 = $28)

As we progress to higher grades, the language of math becomes a little more complex, but the syntax remains the same.

Suppose a student is asked to find “ what percent of 144 is 36?”. Replacing the word “what” with w, “percent” with divided by 100, “of” with multiplication and “is” with equals gives us the new math phrase (w/100) x 144 = 36.

There are numerous such examples and learning the idea of math as a language is like having a personal math tutor freely available at any time!

Here’s a normal conversation between a student and a typical online Geometry tutor at eTutorWorld and then lets decide for ourselves whether Geometry is a study or can be made into a child’s play with appropriate tutoring.

G T: Geometry is Easy, isn’t it?

Student: But I find Geometry to be very challenging. It’s difficult to study and learn those theorems and proofs.

G T: OK! Let us NOT study Geometry…instead have some fun with it.

Student: You kidding me!

G T: Geometry is tricky; it’s thought-provoking and a lot of fun to play with.

Student: You must be a magician; can you put that straight for me.

G T: Here is how: Remember the first day you held a ruler and drew a straight line with it on a paper and rejoiced, and then traced a circle with a wet finger around a glass on the dining table…all of it sure was fun. Geometry is about points, lines, shapes and much more. .

Student: That is interesting. You know there was a time when I found it difficult to read the analog clock, till I learnt it, and that was fun too…like geometry, you would say!

G T: You got it! And this is how an online geometry tutor like me can progress with students like you who find studying geometry very tough. Simple day to day problems are made easy and interesting. Geometry begins with points and encompasses lines, shapes, patterns, angles…..

Student: Also figures, sizes, surfaces, planes and solids.

G T: Yes, all about space…measuring lengths, areas and volumes, perimeter, surface areas and lot more. Sounds intriguing, doesn’t it?

Student: Yes! We learnt as we drew, a Sun is a circle, the sails of a sailboat are triangles, and a notebook is a cuboid. It was so much fun! But I kind of mess up when I deal with higher stuff. You know what I mean? And I can’t figure it out all by myself, and not many friends around me are able to help either!

G T: That is exactly when an online geometry tutor appears like a genie. He can help you on this by taking you on a step by step journey, which will turn out to be a combination of drawings and calculations as well as Arts and Math. Then you will wonder whether geometry is a study, or is it  just  child’s play!!!

Student: Now it is my chance to make geometry sound like lots of fun to work with. Let us go back to the clock….The face of a clock is a circle, and if the hour hand rests on 12, the minute hand traces 360 degrees in a circle. Isn’t that right?

G T: Wow! You are getting there really fast!

Student: You mentioned something about everyday problems; can you explain that bit too? How do we apply geometry in real life?

G T: Sure! Online geometry tutoring will take you step by step in understanding the problem, breaking it down into simple steps, introducing geometrical formulae, relating the formulae to the problem and then let you come up with a solution…Abra-ca-dabra. For example, if you need to build a fence around your garden…what length of mesh would you buy?

Student: Ahem!

G T: This is how online tutoring can help you build up your own skills:First with helping you find the shape of the garden., Let us say, a square in this case, then finding the length of just one side, making it four times, which will give you the perimeter and that turns out to be the length of the mesh we need to order!

Student: Fairly simple and interesting! But how will I get to  understand high school geometry?

G T: An high school online geometry tutor will first assess your present knowledge in geometry and then will build upon it by introducing geometrical concepts in an interesting way that learning geometry will be simple and fun. At eTutorWorld we have the best of online geometry tutors who have successfully proved to students the world over that geometry is not  a study, but  child’s play!

You too can click here to get started.