Depending on your grade level and age; geometry means something completely different. In kindergarten kids love it because it's all about bringing meaning to shapes and things around them. In high school it can be the bain of a teenagers existence. I have always thought geometry is very logical; you just need to put some time into understanding. You will find all grade levels covered here including primary, elementary, middle school, and high school.
Elementary Through Middle School Level
- 2D and 3D Area, Volume and Surface Area - We look at the different measures that can be assessed on two- and three-dimensional objects. We define these and show you how to determine the proper formula to use with each of the different shapes.
- Angle Sums and Exterior Angles of Triangles - This is a really helpful skill when you are working with wood or designing just about anything. The sum of exterior angles is three-hundred sixty degrees.
- Angles in a Multi-Step Problems - We show how to approach missing angle problems from all types of directions. We work off of the concept of adjacent, complementary, supplementary, and vertical angles.
- Area and Perimeter of Triangles, Parallelograms and Trapezoids - We show you how to find these two measures on all the three different shapes. There is a slightly different approach for each.
- Area and Circumference of a Circle - We show you how to find both these measures after explaining what pi is.
- Basic Missing Piece Patterns - This helps youngsters understand patterns with basic geometric shapes.
- Classify and Identify Regular Polygons - We show you how to name polygons based on the number of sides and corners that a shape has.
- Complementary and Supplementary Angles - Complementary angles have a sum of ninety degrees. Supplementary angles have a sum of one-hundred eighty degrees.
- Decomposing Three-dimensional Figures - This is where the concept of geometric nets finishes or starts for that matter.
- Dilations, Translations, Rotations, and Reflection - We watch all these geometric shapes boogie around the coordinate plane. We show you how to classify each movement.
- Distance Formula - We can use this to find the distance between two points on a coordinate plane. It basically just applies the Pythagorean theorem to this system.
- Drawing and Tracing Geometric Shapes - This helps students become more familiar with the shapes and makes them much easier to name and use.
- Drawing Geometric Shapes with Given Conditions - This is exactly what architects do every time they design a custom home or building.
- Find The Volume Of A Right Rectangular Prism - You just need to find the product of the three measures: length, width, and height.
- Finding the Area of Composite Shapes - These are shapes that are a bit irregular. We show you how to break them down into smaller parts.
- Half Pre-Symmetry - This is the step that students need to understand before they can understand the concept of symmetry.
- Lines of Symmetry in Two-dimensional Figures - We show you where to place these and how to manage these types of problems.
- Identify and Classify Angles - There are really five different classifications of angles. We show you how to approach these problems.
- Lines and Angles - We show you how to identify different relationships between angles.
- Liquid Volume and Mass Word Problems - This topic will help students learn how to locate measures that they need to understand in order to compute the final solution.
- Make Them the Same - This simple concept is really helpful as we shift from basic to advanced geometry skills.
- Measure Area By Counting Units - This a more elementary approach to common geometry problems.
- Measuring Lengths using Rulers - You will learn how to use a standard ruler to measure length.
- More or Less Items or Objects - Learn to compare groups of objects.
- One to One Relationships - This works on the basic concept of connecting two items together.
- Parallel and Perpendicular Lines - You will learn how to identify them and what they mean toward solving basic geometry problems.
- Partitioning Circles and Rectangles - Learn how to split these based on a set of strict directions.
- Partition Circles and Rectangles In Halves, Quarters, and Other Fractions - This will help you solve basic geometric sectioning problems.
- Patterns Through Colors - In most cases the problems are just asking you to determine what comes next a sequence.
- Polygons in the Coordinate Plane - Based on a series of plotted points you will need to name geometric shapes on a plane.
- Properties of Rotations, Reflections, and Translations - Learn how to spot all of these movements of geometric shapes and how to calculate their position base don the type of trajectory.
- Pythagorean Theorem On Coordinate Systems - This can be used to find the distance between points or multiple points.
- Pythagorean Theorem Proofs and its Converse - It basically tells us that the square of the longest side is each to the some of the square of the other two lengths of the triangle.
- Pythagorean Theorem - You will determine when you can use this formula based on the geometric shapes that you are working with.
- Pythagorean Theorem Word Problems - You will quickly start to realize that this simple theorem has some many different applications available.
- Relative Position - Where is one thing located in respect to another.
- Recognize Area as Additive - This is really helpful when you have some really weird irregular shape that you need to find the area of.
- Scale Drawings of Geometric Figures - If they have a six sided shape, it is not that hard to make scale drawings.
- Segments, Rays, Lines - You will learn how identify and name these measures.
- Shape Find and Following Directions - This is for younger children working on the skill.
- Shape Sorting - The is the first step of identifying two things that are the same.
- Simple Patterns - A great way to introduce this concept to students.
- Symmetry of Objects - Learn how to help students find balance between objects.
- The Attributes of Two-dimensional Figures - Outside of a circle, all figures have a dimension of at least one line segment.
- Two-dimensional Congruent Figures - How to spot them and prove they are congruent.
- Understanding Congruent Shapes - We show you what this means at what you can do in geometry with congruent shapes.
- Understanding Visual Fractions of Shapes - We show you how to name and recognize fractions of a group.
- Understanding Similar Figures - These are not always the same size.
- Unknown Side Lengths in Right Triangle - Guess what theorem we are going to use here?
- Using Similar Triangles to Find Slope - They should have a corresponding slope.
- Which is Smaller? - A simple comparison for you to build off of.
- Writing Expressions for Geometric Sequences - This helps use better under the data by writing a general rule.
High School Level Worksheets
- Angles in Inscribed Right Triangles and Quadrilaterals - We jam a triangle into a circle in most cases.
- Area and Perimeter in the Coordinate Plane - Most students find this much easier to deal with then they first thought.
- Area of Sectors of A Circle - You learn how to calculate the area.
- Basic Geometry Definitions - These are general rules that apply to all things geometry. This section will help you understand the basic vocabulary you will need for writing proofs.
- Cavalieri's Principle - It basically says that if two shapes with the same volume are the same height, so are their cross-sectional area. This is used often in Biology.
- Circles: Inscribed Angles, Arcs and Chords - We look at common circle geometry terms at help students learn to spot them.
- Congruent Triangles: SSS and SAS Theorems - We look at these specific theorems and apply them.
- Congruent Triangles: ASA and AAS Theorems - We explore different theorems that will be a big part of proof writing.
- Constructing and Using Tangent Lines - These are used to understand rate changes in functions.
- Corresponding Angles of Similar of Triangles - We transition from worrying about side lengths to focusing on angles.
- Cos and Sin Trigonometric Ratios - This helps you better understand the value of sides and angles in triangles.
- Cross-sections of Three-dimensional Objects - We explain the concept which is tough to do in a two-dimensional environment.
- Dilations and Parallel Lines - These can be used to find various measures in a coordinate system.
- Dilations and Scale Factors - This helps build upon the concept of drawing things to scale.
- Drawing Transformed Figures - You will be given directions and you will create new shapes based on them.
- Equations of Ellipses - We show you how to write them and understand them.
- Equations of Hyperbolas - We shift over to one of my favorite shapes.
- Finding the Equation of Circles - Students will get an opportunity to learn the basic equational form of these shapes.
- Finding the Equation of a Parabola - Where does it sit and how do you use them?
- Finding Midpoints of Line Segments - We show you how to find the mathematical center.
- Geometric Proofs on Lines and Angles - This is a nice place to start with writing proofs.
- Geometric Transformations within a Plane - We take a look at the math behind these movements.
- Graphing Complex Transformations - We learn how to visualize the twists and turns that shapes make.
- Inscribing Shapes in Circles - This looks impossible to calculate when you first view it.
- Making Bisectors of Angles and Lines - You will learn how to draw and calculate them.
- Making Perpendicular and Parallel Lines - This is done with precision.
- Measurements of Arcs - How to calculate them and understand what they mean.
- Perimeter of Polygons with Inscribed Circles - This gives you a nice reference to work off of.
- Proving the Formula A = 1/2 ab sin(C) - When working with the area of triangles.
- Proving Theorems of Parallelograms - Students seem to find this to be one of the easier proofs.
- Proving Triangle Congruence - We approach this one from a wide variety of ways.
- Proving Triangle Theorems - This is a collection of all the different theorems that we have used.
- Rigid Motions to Transform Figures - When figures make these movements, they hold onto their length of sides and angles.
- Rigid Motions and Congruent Triangles - In this case we are comparing two figures.
- Rotations, Reflections, and Translations of Geometric Shapes - Another look at all these moves that figures can make.
- Similarity of Circles - What does it mean and how do we use it to our advantage?
- Similarity Transformations - This will be helpful when writing proofs.
- Slopes of Parallel and Perpendicular Lines - You will use this skill with proofs in the future.
- Tangent Ratios - Given an angle, you will be able to find the length of unknown sides.
- Triangle Proofs - This puts all that work together to help you achieve advanced skills.
- Triangles (Similarity and Congruence) - What is the difference and what can you do with it?
- Trigonometric Ratios and the Pythagorean Theorem - We will contrast and compare the relationship.
- Using Coordinates to Prove Theorems - This is a good tool to verify position.
- Using Density in Real-life Situations - This topic has a great deal of relevance to science related situations.
- Using Geometry in Design Problems - Time to see what designers and architects go through on a daily basis.
- Using Shapes and Measures to Describe Objects - We work on the language that we use to communicate about objects.
- Using Sine and Cosine - We will explore these ratios graphically and mathematically.
- Volume of Cones and Spheres - You will learn how to calculate their volume and the measures that are required to do so.
- Volume of Cylinders and Triangular Prisms - Probably the most complex portion of this is making certain you have the correct measure to work with.
What is Geometry?
Geometry is one of the oldest fields of science and can be traced back to ancient Greek. Geometry was used to better understand the world we live in, and the practice continues as of today. Geometry is a Greek word. In Greek, 'geo' stands for 'earth' and 'metric' stands for 'measure'. So, it can be seen as the study of measuring the Earth or in other words, the world around us.
Geometry is the branch of mathematics that educates us about the sizes, shapes, configurations, and manipulation of two-dimensional and three-dimensional shapes. Geometry studies the all-round aspects of shapes such as how much space a shape can hold, how it is positioned, and how it can be measured to better understand the surroundings.
Geometry is not subject limited to the classrooms or textbooks; it is used and observed by all of us daily by each of us. Your brain is constantly making geometric calculations as you get off your bed in the morning or try to parallel park a car. You can observe geometry in the architecture of the tall skyscrapers around you or in the structuring of a robot. Geometry is a cornerstone of art, architecture, engineering, astronomy, and other major fields of sciences.
The basic concepts of geometry include shapes and solids, lines and line segments, the circumference of a circle, and angle and triangles. Advanced concepts of geometry involve radians, trigonometry, conic sections, and coordinate grids.