Geometry is the area of mathematics that is concerned with the shapes around us. Geometry deals with the nature of these shapes as well as what they tell us about the world. These shapes relate to everything in existence, from biology to the design of buildings and other man-made objects. Learning geometry will help you to acquire important problem-solving skills and will help you with other areas of mathematics as it is connected to various other math topics.
When studying geometry, your first step will be to learn understand its fundamentals. You should focus on the areas below.
Main Topics in Geometry
• Lines and Line Segments This area covers lines and segments along with intersecting and concurrent lines. This topic covers points and rays as well.
• Congruence This is one of the fundamental areas of geometry. It refers to the fact that if you can rotate one figure to make it identical to another figure, then those two figures are considered congruent.
• Angles Here is where you will learn about angles and how they relate to each other. You will also learn to identify right, acute and obtuse angles.
• Triangles and Quadrilaterals This will help you get a better understanding of how triangles and quadrilaterals relate to each other.
• Area, Volume and Perimeter Among the fundamental areas of geometry are the formulas for calculating the area, volume and perimeter of various shapes and solids including parallelograms and triangles.
• Circles This area deals with calculating the circumference, diameter and radius of a circle.
• Quadrilaterals You will learn to identify and describe different types of quadrilaterals including squares, rectangles and parallelograms.
• Dissections and Proof This topic involves using the properties of figures to solve geometry problems and to prove their solutions.
• Pythagorean Theorem The Pythagorean theorem is one of the foundations of mathematics and is one of the ways in which mathematics differs from other
sciences. Pythagorean theorem involves starting with an assumption and then drawing your conclusions from a series of logical steps. If you make correct assumptions and follow logical steps to your conclusion, then your result can be considered trustworthy and may be used to prove other results. A result that has been proved becomes a theorem.
Tips for Learning Geometry
• Work on Your Geometry Vocabulary Do you know what a ray is? Do you know what a vertex is? These are important concepts in geometry that are useful for understanding problems and finding solutions to them. Other geometry terms that you should learn include rhombus, trapezoid and symmetry.
• Get the Right Tools You will need a protractor, preferably one that is transparent. Clear plastic protractors make reading and measuring angles far easier. A ruler is also important, preferably clear as well. A clear ruler allows you to extend your lines, which makes measuring them easier. Make sure that both your ruler and protractor are labeled with both inches and centimeters as different equations may have different units of measurement. You will want a tool that is useful for both. A compass will be your next most important tool; compasses allow you to make symmetrical curved lines. A good pencil is important for drawing fine lines. Your best option is a technical drawing pencil that has a .05mm lead.
• Learn to Identify Shapes and Angles Learn the properties of plane figures like circles and rectangles, as well as the properties of solid shapes such as cylinders and spheres.
• Learn to Identify Triangles by Their Angles For example, an angle that has one 90-degree angle is a right angle. You should also learn to identify acute and obtuse angles.
• Learn to Identify Triangles by the Lengths of Their Sides An equilateral triangle has sides of the same length, how is an isosceles triangle different? What is a Scalene triangle? Learn the differences so that you can categorize the different types of triangles.
• Understand Area This is the measurement of how much space something takes up in two dimensions. You could compare the size of your backyard versus a neighbor’s smaller or larger backyard as a way to understand area. How do you measure the space that an object takes up? One way to do this is with unit squares. Define an amount of area; a 1-inch square is a good example. You can then see how many 1-inch squares fit within the space that you want to measure. If five squares fit (without overlapping), then you can say that the object takes up five square inches.
• Understand Perimeter The term refers to the boundary of a shape. When you are calculating perimeter in geometry, you are determining the length of a shape’s boundary. This is done by adding the lengths of the different sides. The total of the sides is equal to the perimeter of the shape.
• Understand Symmetry This is one of the fundamental areas of mathematics. Symmetry can exist in algebraic calculations and in geometric designs. It is important that you examine geometric symmetry by creating designs and looking at their properties.
• Understand Similarity While the meanings of symmetry and similarity are close in standard English, the words carry different meanings in geometry. You should work on understanding the definition of similarity and how it is applied to triangles and triangle trigonometry.• Memorize FormulasYou will want to remember formulas, but it is more important to remember how to arrive at a formula. For example, understanding the formula for finding the area of a rectangle and understanding the relationship between rectangles and triangles can help you to calculate the area of a triangle. By learning basic formulas, you can make learning advanced geometry easier.
Joshua L. Davis III is a math teacher, math tutor and mentor who has 18 years of public school teaching experience and 38 years of tutoring experience. Because I am always growing by learning and sensing how my students learn and process information, I have developed an exceptional ability to teach and explain math in a way that anyone can understand. I love teaching math and interacting with other people. What I love most is that I am always learning new instructional approaches from all of my students everyday.