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Cheat Sheet

Geometry Workbook For Dummies

The helpful geometry symbols, formulas, and principles in this cheat sheet ease your learning curve. Working with geometry means never being bored: You get to work with lines, angles, and arcs; triangles, circles, and polygons; two-dimensional and 3-D objects; and you even get to use graphs!

Geometry Symbols

If you’re studying geometry, you’re seeing symbols everywhere — symbols for arcs and angles, lines and triangles as well as symbols for the relationships between lines and angles and so on. Following is a list of common geometry symbols:

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Triangle Terminology for Geometry

Triangles are at least a third of geometry (tri = three . . . a little geometry humor). But, seriously, the sides and angles of triangles may have all sorts of relationships to each other, and the following list shows the abbreviations that indicate these relationships:

  • SSS: Side-side-side congruency

  • SAS: Side-angle-side congruency

  • ASA: Angle-side-angle congruency

  • AAS: Angle-angle-side congruency

  • HL(R): Hypotenuse-leg-(right angle) congruency

  • AA: Angle-angle similarity

  • SSS~: Side-side-side similarity

  • SAS~: Side-angle-side similarity

  • CPCTC: Corresponding parts of congruent triangles are congruent

  • CSSTP: Corresponding sides of similar triangles are proportional

Geometry Formulas for 3-D Objects

You know those big, 3-D movie blockbusters? They’d be nowhere without geometry . . . geometry and those weird glasses. Knowing the formulas for 3-D objects is key in the real world of geometry, and those formulas are provided here:

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Geometry Formulas and Rules for Triangles

The three-angled, two-dimensional pyramids known as triangles are one of the building blocks of geometry (however three-cornered they may be). Triangles, of course, have their own formulas for finding area and their own principles, presented here:

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Triangles also are the subject of a theorem, aside from the Pythagorean one mentioned earlier. The Altitude-on-Hypotenuse Theorem makes dealing with triangles just a bit easier. It states that if you draw an altitude from the right angle of a right triangle to the hypotenuse, dividing the hypotenuse into two segments, then the altitude squared is equal to the product of the two segments of the hypotenuse. A leg of the right triangle squared is equal to the product of the segment of the hypotenuse nearer the leg and the entire hypotenuse.

Geometry Formulas and Theorems for Circles

Geometry isn't all about pointy angles — there are circles, too. What’s interesting about circles isn’t just their roundness: Become familiar with geometry formulas that help you measure angles around circles, as well as their area and circumference. Following are the formulas you need to know about circles:

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And, circles have their own theorems as well:

  • Chord-Chord Power Theorem: When two chords intersect, the products of the measures of their parts are equal.

  • Tangent-Secant Power Theorem: When a tangent and a secant meet at an external point, the measure of the tangent squared is equal to the product of the secant’s external part and its total length.

  • Secant-Secant Power Theorem: When two secants meet at an external point, the products of their external parts and their total lengths are equal.

Geometry Formulas for Polygons

Polygons, those many-sided objects so popular in geometry circles, are subject to their own formulas that help you find the area and angles of various geometrical shapes. Have a look at the most common formulas for working with polygons:

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Coordinate Geometry Formulas

When you work in geometry, you sometimes work with graphs, which means you’re working with coordinate geometry. Becoming familiar with the formulas and principles of geometric graphs makes sense, and you can use the following formulas and concepts as you graph:

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