# Geometry Study Guide for the Math Basics

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## How to Prepare for the Geometry Questions on a Math Test

### General Information

Geometry is just a fancy name for the study of lines and shapes. There are certainly additional difficult principles and topics, but we have the basics here. You’ll need to master these before tackling more advanced concepts.

(Please note that if a figure is labeled “example” in this guide, it may not be the *only* representation of that figure, but is one of them.)

### Points and Lines

A *point* in geometry is a location. It has no length, width, or depth. We use a dot and a capital letter to show a point.

A line *segment* is defined by two points and all the points between them. The two points are called *endpoints* of the segment. A segment has one dimension: length. To write a segment, place a bar over the two endpoints. \(\overline{AB}\) or \(\overline{BA}\) is this segment:

A *line* extends in both directions without end. To write a line, place a bar with two arrows over any two points of the line. \(\overleftrightarrow{AB}\) or \(\overleftrightarrow{BA}\) is the line:

A *ray* starts at one endpoint and extends without end in only one direction. To write a ray, place a bar with an arrow pointing to the right over two points: the endpoint and any other point (in that direction). \(\overrightarrow{AB}\) is the ray:

Note: you *cannot* write a ray with the arrow pointing to the left like \(\overleftarrow{BA}\). Also, the order is important. \(\overrightarrow{BA}\) is not the same as \(\overrightarrow{AB}\). The first letter is always the starting point of a ray.

Two lines, segments, or rays are *perpendicular* if they form a *right angle* (see below). Use the symbol \(\perp\) to denote perpendicularity. For instance, if \(\overline{AB}\) is perpendicular to \(\overline{CD}\), you can write \(\overline{AB} \perp \overline{CD}\).

*Examples:*

Two lines are *parallel* if they never intersect. If \(\overleftrightarrow{AB}\) is parallel to \(\overleftrightarrow{CD}\), you can write \(\overleftrightarrow{AB} \parallel \overleftrightarrow{CD}\).

*Examples:*

### Plane Shapes

In geometry, a *plane* is a flat two-dimensional surface that extends infinitely far. The two dimensions are length and width. So, *plane shapes* are “flat” shapes, like squares, circles, and triangles.

#### Common Shapes

A *polygon* is a closed surface on a plane bounded by line segments called sides.

*Examples:*

A *regular polygon* is a polygon in which all segments and interior angles are congruent.

*Examples:*

A *triangle* is a three-sided polygon.

*Examples:*

*Quadrilaterals* - four-sided polygons

A *parallelogram* is a type of quadrilateral where opposite sides are parallel and congruent. Opposite angles of a parallelogram are also congruent.

*Examples:*

A *rectangle* is a parallelogram with four right angles.

*Examples:*

A *rhombus* is a parallelogram in which all four sides are congruent.

*Examples:*

A *square* is a parallelogram which is both a rhombus and a rectangle (all sides are congruent and all angles are right).

*Examples:*

A *trapezoid* is a quadrilateral with *only* one pair of parallel sides.

*Examples:*

*Polygons with more than four sides*

\(^1\) A polygon with 11 sides may also be called an *endecagon* or an *undecagon*.

#### Measuring Shapes

The *perimeter* is the total distance around a polygon. To find the perimeter, just add up the lengths of all the sides. If the polygon is regular (all sides are congruent) and the length of one side is \(s\), then multiply the number of sides by \(s\) to find the perimeter. For example, the perimeter of a regular pentagon is \(P_\text{reg pentagon}=5s\)

The *area* of a polygon is the number of square units which can fit within it. Reference these figures when reading the table.

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