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Geometry Basics

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What Is a Geometry Proof?

A geometry proof — like any mathematical proof — is an argument that begins with known facts, proceeds from there through a series of logical deductions, and ends with the thing you’re trying to prove. [more…]

Getting to Know the Five Simplest Geometric Objects

The study of geometry begins with the definitions of the five simplest geometric objects — point, line, segment, ray, and angle — as well as two extra definitions [more…]

Getting to Know Points

Although individual points have no features, when you group them, you can create several different types of points: collinear, non-collinear, coplanar, and non-coplanar. Each type merits an explanation [more…]

Getting to Know Lines

There are different types of lines (or segments or rays) or pairs of lines (or segments or rays). You can identify single lines based on the direction they’re pointing [more…]

Getting to Know Planes

When two geometric planes interact with each other, it is in one of two ways: as parallel planes or as intersecting planes. Here are the definitions for these two types of relationships between a pair [more…]

Getting to Know Angles

Angles are one of the basic building blocks of triangles and other polygons. There are five types of angles: acute, right, obtuse, straight, and reflex. You see angles on virtually every page of any geometry [more…]

Getting to Know Angle Pairs

Adjacent angles and vertical angles always share a common vertex, so they’re literally joined at the hip. Complementary and supplementary angles can share a vertex, but they don’t have to. Here are the [more…]

How to Measure Line Segments

To find the measure or size of a segment, you simply measure its length. What else could you measure? After all, length is the only feature a segment has. You’ve got your short, your medium, and your long [more…]

How to Measure Angles

Measuring angles is pretty simple: the size of an angle is based on how wide the angle is open. Here are some points and mental pictures that will help you to understand how angle measurement works. [more…]

Adding and Subtracting Segments and Angles

Adding and subtracting segments and angles isn’t exactly rocket science. But it is important because this geometric arithmetic comes up in proofs and other geometry problems. Here’s how it works: [more…]

Geometry Symbols You Should Know

Using geometry symbols will save time and space when writing proofs, properties, and figuring formulas. The most commonly used geometry symbols and their meanings are shown below. [more…]

Bisecting and Trisecting Segments

Bisection and trisection involve cutting something into two or three equal parts. If you’re a fan of bicycles and tricycles and bifocals and trifocals — not to mention the biathlon and the triathlon, bifurcation [more…]

Bisecting and Trisecting Angles

The terms angle bisection and angle trisection describe two ways in which you can divide up an angle equally into two (or three) smaller, congruent angles. Their definitions are often used in proofs. [more…]

Geometry Formulas You Should Know

Below are several of the most important geometry formulas, theorems, properties, and so on that you use for solving various problems. If you get stumped while working on a problem and can’t come up with [more…]


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