Take a guided, problem-solving based approach to learning Geometry. These compilations provide unique perspectives and applications you won't find anywhere else.
Sharpen your skills with these quizzes designed to check your understanding of the fundamentals.
Mathematics is filled with shapes that are kaleidoscopic in variety. Wielded since ancient times, the power of geometry helps us examine and measure these shapes.
Forgive us for being obtuse, but this is a cute concept, and we think it’s right for you.
If the area of a square is 144, what is the perimeter of the square? If a square and a circle have the same perimeter, which of them will have a greater area?
Overlap, inscribe, and circumscribe a collection of simple geometric shapes to make a complex, composite figure.
What is the volume of a sphere of radius 5? If we make a cylinder two times taller, and its radius three times bigger, how many times larger would it become in volume?
A spherical balloon is inflated until its volume becomes 27 times its original volume. How much does its surface area increase?
Given a triangle with side lengths of 5, 12, and 14, is the largest angle in the triangle acute, right, or obtuse? Geometric knowledge helps us deduce much about triangles from limited information.
Can a scalene triangle be obtuse? Is an equilateral triangle always acute?
If you want to find similar triangles, use only SSS, SAS and AAA. Don't make an ASS of yourself.
You know that Area = base x height / 2, but what other ways are there to find the area of a triangle? Brace yourself for some potent formulae.
What do the orthocenter, centroid, and circumcenter share in common? They lie on the Euler line!
These shapes have four sides and 360° of interior angle goodness.
Similar polygons have the same shape, but not necessarily the same size. Are rectangles with dimensions 8 x 5 and 25 x 40 similar?
With equal angles and equal side lengths, what more could you want from a polygon?
Convex and concave, regular and irregular, similar and congruent – learn every variety of polygon you can encounter.
What is pi? If the area of a circle is 49π, what is its circumference? If a circle is inscribed in a square, what is the ratio of the areas of the circle and the square?
A tangent to a circle is a line intersecting the circle at exactly one point. Can you prove that the line from the center of the circle to the point of tangency is perpendicular to the tangent line?
Learn about packing shapes neatly into others, and the resulting geometric properties.
Explore how simple equations have graphical implications starting with the equation of a line.
In the 1600s, René Descartes married algebra and geometry to create the Cartesian plane.
Parabolas, ellipses, and hyperbolas, oh my! Learn about this eccentric bunch of shapes.
Append a z-axis to the 2-dimensional plane and conquer the realm of 3-dimensional space.
SOH-CAH-TOA! Have you heard the call of the trig function? Use them to navigate the trickier sides (and angles) of geometric shapes.
Plot the six different trig functions, discover their illuminating interactions, and ride the wave!
Equations with trigonometry in them can look scary, but that's nothing that a quick little substitution can't fix.
Trigonometric problem solving culminates in this chapter. Leave no side and no angle unmeasured!
Trigonometric identities bring new life to the Pythagorean theorem by re-envisioning the legs of a right triangle as sine and cosine.
These are your basic building blocks for solving trigonometric equations and understanding how the pieces fit together. Using these identities can make sense of even the scariest looking trig.
These formulas explain how to add and subtract trigonometric functions (and their arguments). If you've got sum time, see what a difference these formulas will make for your trig toolkit.
So, you've memorized your fundamental identities, but how can you prove the more obscure ones? See how to apply the basic building blocks of trig to understand deeper relationships.
Vectors allow you to represent quantities with both size and direction, such as the velocity of an airplane. Better yet, they do so in a mathematically-useful way. Dive in to see how!
The dot product (also known as the scalar product) is an operation on vectors that can tell you the angle between the vectors.
The cross product is a fundamental operation on vectors. It acts on vectors in three dimensions and results in another vector in three dimensions which is perpendicular to both of the other vectors!
What is the volume of a sphere of radius 5? If we make a cylinder two times taller, and its radius three times bigger, how many times larger would it become in volume?
A spherical balloon is inflated until its volume becomes 27 times its original volume. How much does its surface area increase?
When shapes get three-dimensional, things get weird. Dive in to learn about the cube, tetrahedron, octahedron, and more.
They say triangles are the simplest polygon, but they're still not all that simple. Dive into this advanced treatment of triangles, and learn beautiful results from Euler's line to Routh's Theorem.
Think circles are straightforward? Well, they're clearly curved, not straight. And they aren't easy, either. Dive into this challenging chapter full of advanced theorems related to circles.
Symmetries are one of the most beautiful part of Geometry. Slide into reflections, rotations, translations, and more, and you'll be on your way to geometric artistry.
Geometry is tricky -- are squares rectangles, or are rectangles squares? There are 10 centimeters in a meter, so how many square centimeters are in a square meter? Get your facts straight here.
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