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# Reference - Circles, Angles, Protractors, Unique Triangles, Area, Volume

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These reference pages cover many geometry topics. I suggest letting your students keep the reference sheets on their desks while working on problems so you can refer them to the correct section instead of reteaching everything if they forgot.

Introduction to Circles

1. Explains radius, diameter, circumference, and area.
2. Explains that radius, diameter, and circumference are all one-dimensional while area is two-dimensional.
3. Explains what pi is.

Circle Equations

1. Derives the circle equations c=pi*d, c=2*pi*r, and a=pi*r^2
2. Explains how to use the circle equations to answer problems such as finding the diameter when given the area, finding the circumference when given the diameter, and so on.

Working with Pi

1. Explains how to write an answer "in terms of pi" and with pi multiplied out.
2. Gives examples of mistakes students often make when solving equations with pi in them.

Introduction to Angles

1. Explains what angles and vertices are.
2. Explains what right angles, obtuse angles, and acute angles are.
3. Explains that angles are measured in degrees and that there are 360 degrees in a full rotation.
4. Explains how to denote right angles.
5. Explains how to name angles using three points.

Measuring Angles with a Protractor

1. Explains how to align the protractor.
2. Explains which set of numbers on the protractor to use.

Angle relationships

1. Explains what complementary, supplementary, congruent, adjacent, linear, and vertical angles are.

Writing Equations to Describe Diagrams

1. Explains how to write and solve equations that describe diagrams.

1. Explains that the sum of the angles of a triangle is always 180 degrees.
2. Explains why you can't have one side of a triangle larger than the sum of the other two sides.

Unique Triangles

1. Creates an analogy between given triangle conditions (SSS, SAS, etc.) and an environment that is possibly too restrictive to move around in, thus creating a unique triangle.

SSA

1. Gives step-by-step instructions on how to determine if SSA conditions determine a unique triangle, two triangles, or no triangles.

Area of 2-Dimensional Shapes

1. Explains what area is.
2. Explains how to find the areas of rectangles, parallelograms, triangles, trapezoids, and irregular polygons.

Volume

1. Explains what volume is.
2. Explains how to find the volume of prisms, pyramids, and spheres.

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12 pages
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