Schools & Districts
All of Shmoop
Cite This Page
Best of the Web
Table of Contents
Basic Geometry Exercises
Basic Shapes & Angles
This is where it all begins: basic shapes, lines, and angles. Read on and let us take you on a magical geometry tour...NameDescriptionExamplePointA single location.Usually drawn as a dot.It is "dim...
Not to be confused with angels, angles are the pointed corners of shapes. Angles can be named three different ways. This angle could be named any of these ways: (counterclockwise) (clock...
Parallel Lines & Transversals
A transversal is a line that intersects two or more other lines. When it intersects parallel lines, many angles are congruent. Let's take a peek at what this means. Lines k and j are parallel. L...
A polygon is any closed figure with three or more straight sides. "Closed" means that there are no gaping holes in it and that all sides connect together.These Are Polygons:These Are Not Polygons:...
Triangles are three sided polygons, but we're sure that you already knew that. The triangle is the most sturdy of polygons. Its strong shape has been used to build buildings and bridges since the...
Quadrilaterals are four sided shapes. The most common include squares and rectangles, but there are loads of others as well. Like triangles, they are classified by their angles and sides. In t...
Angles in a Polygon
As we discussed before, the three angles of a triangle always add up to 180°.In each case . By the way, means "the measurement of angle A".To find the total number of degrees in any...
Similar figures have the same shape, but might not be the same size. When two shapes are similar, their corresponding sides are proportional (see ratios and proportions) and their correspondin...
Perimeter & Circumference
The perimeter of a shape is the distance around the outside of the figure. It's pretty simple; just add up the lengths of each side. Perimeter is often used to find the measurements needed to put b...
Let's go over these formulas one more time.Formulas for different shapes:Area of Rectangle = Base x HeightArea of Triangle = ½(Base × Height)Area of Parallelogram = Base × HeightArea of Trapezoi...
Area of Irregular Shapes
In real life figures are often irregular shapes - a little bit messy. Think of your messy bedroom once more ‐ is it a perfect rectangle? The trick: break these figures into shapes that you know w...
3D Objects (Prisms, Cylinders, Cones, Spheres)
Three‐dimensional objects are the solid shapes you see every day, like boxes, balls, coffee cups, and cans. Here are some helpful vocabulary terms for solids: Base: the bottom surface of a solid...
Volume of Prisms & Cylinders
The volume of a solid is the amount of space inside the object. It's how much water fits inside a bathtub, how much sand fills a bucket, or how much soda your friend can chug and hold in his stomac...
Volume of Pyramids & Cones
The formula for the volume of pyramids and cones tells you how much space is inside each object.For these two solid shapes, the volume formula is the same: it's one third of the area of the ba...
Volume of Spheres
To find the volume of a sphere, follow this simple formula (which took a brilliant ancient Greek mathematician named Archimedes years to derive):Volume of a Sphere = 4/3π x radius cubed = 4/3πr3
The surface area of a solid is the area of each surface added together. There are few formulas to memorize (w00t!). The keys to success: make sure that you don't forget a surface and that you have...
A long time ago, in ancient Greece, a brilliant guy named Pythagoras discovered something pretty amazing and useful.Pythagorean Theorem: a2 + b2 = c2In a right triangle the sum of the squares...
© 2013 Shmoop University, Inc. All rights reserved. We love your brain and respect your privacy. |
© 2013 Shmoop University, Inc. All rights reserved. We love your brain and respect your privacy.