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# Lesson 5.2: Segments, Lines, Rays and their Relationship

## Symbols

$\text{multipurpose indicator}$

$\text{directly over symbol}$

$\text{segment}$

$\text{ray}$
⠪⠒⠒⠕

$\text{line}$
⠫⠕

$\text{termination indicator}$

$\text{∥ parallel}$
⠫⠇

$\text{⊥ perpendicular}$
⠫⠏

## Explanation

In braille some shapes may need to be modified to represent symbols in print. This is true for shapes that are positioned above other symbols in order to represent the symbols for a segment, line, or ray. Typically these shapes are defined by two distinct points on the segment, line, or ray. In print, the symbol for a segment, line, or ray is then placed directly above the two letters used to name the shape. A segment symbol is a horizontal bar above the letters. A line is a horizontal bar with arrows on either side of the bar pointing to the left and to the right indicating that the line goes on forever in both directions. Finally, a ray has a horizontal bar with an arrow typically only on the right side indicating that the ray starts at one point and continues onward forever in the direction of the other letter used to name the ray.

Representing these shapes is a five step process.

Step 1: The portion of the expression being modified must begin with the multipurpose indicator, dot five.
Step 2: The expression that is to be changed is brailled next.
Step 3: The directly over symbol, dots one two six, follows the expression.
Step 4: The symbol which appears directly over or directly under the expression is brailled.
Step 5: The termination indicator, dots one two four five six, indicates the position where the modification ends.

Two symbols that are typically used with the symbols for segment, line, and ray are the parallel and perpendicular symbols. In print, the symbol for parallel is two vertical lines beside each other indicating two lines that never cross. In braille the symbol for parallel is a two-cell symbol made up of the shape indicator followed by dots one two three. The symbol for perpendicular in print is a vertical line with an intersecting horizontal line at the bottom to indicate two lines that intersect at a right angle. In braille, the symbol for perpendicular is a two-cell symbol made up of the shape indicator followed by one two three four.

In the following examples and exercises, the symbols for segment, ray, and line are superscribed over the letters that make up the segment, ray or line. These geometric shapes are typically named using two letters, although you may see them with more. The braille configurations for the segment, ray, and line are described below.

A segment is represented by a horizontal bar, dots one five six.

A ray is represented by the shape indicator followed by the barb of an arrow. This would be dots one two four six followed by dots one three five. The line is represented by the shape indicator followed by an arrow with barbs on both ends. This would be dots one two four six, dots two four six, dots two five, dots two five, and dots one three five.

### Example 1

$\stackrel{‾}{\mathrm{AB}}$

dot five, cap A, cap B, directly over symbol, dots one five six for the horizontal bar, termination indicator

⠐⠠⠁⠠⠃⠣⠱⠻

### Example 2

$\stackrel{\to }{\mathrm{AB}}$

dot five, cap A, cap B, directly over symbol, the shape indicator then dots one three five for the arrow to the right, termination indicator

⠐⠠⠁⠠⠃⠣⠫⠕⠻

### Example 3

$\stackrel{↔}{\mathrm{AB}}$

dot five, cap A, cap B, directly over symbol, the shape indicator then dots two four six dots two five dots two five dots one three five for the horizontal bar and arrows to the left and right, termination indicator

⠐⠠⠁⠠⠃⠣⠫⠪⠒⠒⠕⠻

### Example 4

$\text{Do}\phantom{\rule{.3em}{0ex}}\stackrel{↔}{\mathrm{AB}}\phantom{\rule{.3em}{0ex}}\text{and}\phantom{\rule{.3em}{0ex}}\stackrel{↔}{\mathrm{BA}}\phantom{\rule{.3em}{0ex}}\text{name the same line?}$
⠠⠙⠕⠀⠸⠩⠀⠐⠠⠁⠠⠃⠣⠫⠪⠒⠒⠕⠻⠀⠠⠄⠁⠝⠙⠀⠐⠠⠃⠠⠁⠣⠫⠪⠒⠒⠕⠻⠀⠸⠱⠀⠝⠁⠍⠑⠀⠞⠓⠑⠀⠎⠁⠍⠑⠀⠇⠊⠝⠑⠦

### Example 5

$\text{Does}\phantom{\rule{.3em}{0ex}}\stackrel{‾}{\mathrm{CD}}\phantom{\rule{.3em}{0ex}}\text{intersect}\phantom{\rule{.3em}{0ex}}\stackrel{‾}{\mathrm{GH}}\text{?}$
⠠⠙⠕⠑⠎⠀⠸⠩⠀⠐⠠⠉⠠⠙⠣⠱⠻⠀⠠⠄⠊⠝⠞⠑⠗⠎⠑⠉⠞⠀⠐⠠⠛⠠⠓⠣⠱⠻⠀⠸⠱⠦

### Example 6

$\parallel$
⠫⠇

### Example 7

$\perp$
⠫⠏

### Example 8

$\stackrel{‾}{\mathrm{MN}}\parallel \stackrel{‾}{\mathrm{XY}}$
⠐⠠⠍⠠⠝⠣⠱⠻⠀⠫⠇⠀⠐⠠⠭⠠⠽⠣⠱⠻

### Example 9

$\stackrel{\to }{\mathrm{PQ}}\perp \stackrel{\to }{\mathrm{PT}}$
⠐⠠⠏⠠⠟⠣⠫⠕⠻⠀⠫⠏⠀⠐⠠⠏⠠⠞⠣⠫⠕⠻