# Unit 14 Shapes and Angles

Raised dots can be used to draw shapes on a page like this:

As you can see, these shapes use many lines and spaces and would be ineffective on an electronic braille display.

When shapes are used in a mathematical context, a shape indicator followed by a letter, number or other character represents the shape. Nemeth rules are followed for code switching, spacing and punctuation.

*Note: Examples in this lesson that are not embedded in UEB have omitted the Nemeth Code switch indicators.*

Shape Indicator | ⠫ |

These common shapes are represented by a shape indicator followed by the first letter of the shape name.

Rectangle | ⠫⠗ |

Circle | ⠫⠉ |

Triangle | ⠫⠞ |

Star | ⠫⠎ |

Diamond | ⠫⠙ |

# Examples:

$\mathrm{\u2606}+\mathrm{\u2606}$⠫⠎⠬⠫⠎

$\mathrm{\u25ef}\mathrm{\u25ef}=\mathrm{\u25ad}$⠫⠉⠀⠫⠉⠀⠨⠅⠀⠫⠗

These common shapes are represented by a shape indicator followed by the number of sides on the shape.

Square | ⠫⠲ |

Pentagon | ⠫⠢ |

Hexagon | ⠫⠖ |

Octagon | ⠫⠦ |

# Examples:

$\mathrm{\u2b20}=5\phantom{\rule{thickmathspace}{0ex}}\text{sides}$⠫⠢⠀⠨⠅⠀⠼⠢⠀⠎⠊⠙⠑⠎

$\mathrm{\U0001f532}\mathrm{\U0001f532}=\mathrm{\u2b21}$⠫⠲⠀⠫⠲⠀⠨⠅⠀⠫⠖

# Spacing

A space is left between a shape and its identifier (related number or letter/s), and a shape and its related identifier are never separated between two lines.

◯ B

⠫⠉⠀⠠⠃

△ ABC

⠫⠞⠀⠠⠁⠠⠃⠠⠉

# Shapes as Signs of Omission

When a shape is used to represent an omission, such as a sign of operation or comparison, numeral, etc., spacing follows the rules of the item it replaces.

# Examples:

$3\mathrm{\u25ef}5=$⠼⠒⠫⠉⠢⠀⠨⠅

$27\times 3=\mathrm{\u2b1c}$⠼⠆⠶⠈⠡⠒⠀⠨⠅⠀⠫⠲

${a}^{\mathrm{\u2b1c}}$

⠁⠘⠫⠲

$\sqrt{\mathrm{\u2b1c}}=7$⠜⠫⠲⠻⠀⠨⠅⠀⠼⠶

# Filled or Shaded Indicator

Any shape that is filled or shaded requires an additional indicator to show the modification. The filled (dots 4-5-6) or shaded (dots 4-6) indicator is placed after the shape indicator and before the shape symbol to represent the additional modification.

Filled Shape Indicator | ⠸ |

Shaded Shape Indicator | ⠨ |

# Examples:

⠫⠨⠙

$\mathrm{\u25b2}$

⠫⠸⠞

$\mathrm{\U0001f7e6}$

⠫⠸⠲

$3\u2064{\displaystyle \frac{\mathrm{\u25b2}}{4}}$⠼⠒⠸⠹⠫⠸⠞⠌⠲⠼

⠠⠭⠀⠫⠨⠙⠀⠠⠽

${6}^{5}=\mathrm{\U0001f7e6}$⠼⠖⠘⠢⠀⠨⠅⠀⠫⠸⠲

# Nemeth Code Switch Indicators

Because a shape is considered a math symbol, Nemeth Code switch indicators are required and punctuation following a shape requires a punctuation indicator.

# Examples:

$\text{Count the}\phantom{\rule{thickmathspace}{0ex}}\mathrm{\u25b3}\text{'s}$⠠⠉⠨⠞⠀⠮⠀⠸⠩⠀⠫⠞⠸⠄⠎⠀⠸⠱⠲

⠠⠇⠑⠞⠀⠸⠩⠀⠫⠢⠀⠨⠅⠀⠼⠢⠸⠆⠀⠼⠆⠈⠡⠫⠢⠀⠨⠅⠀⠿⠀⠸⠱

$\text{The perimeter of a}\phantom{\rule{thickmathspace}{0ex}}\mathrm{\U0001f532}=4\mathrm{s}$⠠⠮⠀⠏⠻⠊⠍⠑⠞⠻⠀⠷⠀⠁⠀⠸⠩⠀⠫⠲⠀⠨⠅⠀⠼⠲⠎⠀⠸⠱

# Angles

An angle is also considered a shape. The shape indicator followed by dots 2-4-6 represent the angle sign and all rules for shapes apply.

Angle | ⠫⠪ |

# Example:

∠ d = ∠ e

⠫⠪⠀⠙⠀⠨⠅⠀⠫⠪⠀⠑

∠ 30°-∠ 15°

⠫⠪⠀⠼⠒⠴⠘⠨⠡⠐⠤⠫⠪⠀⠼⠂⠢⠘⠨⠡

Because an angle is considered a math symbol, Nemeth Code switch indicators are required.

# Examples:

Measure ∠ q

⠠⠍⠂⠎⠥⠗⠑⠀⠸⠩⠀⠫⠪⠀⠟⠀⠸⠱

Are ∠ M and ∠ N congruent?

⠠⠜⠑⠀⠸⠩⠀⠫⠪⠀⠠⠍⠀⠠⠄⠯⠀⠫⠪⠀⠠⠝⠀⠸⠱⠀⠤⠛⠗⠥⠢⠞⠦

# Brain Boost

# Modified Triangles

When a triangle is defined by its type, an additional modification is needed to identify the triangle by its structure.

Structural Shape Modification Indicator | ⠨ |

Termination Indicator | ⠻ |

A structural shape modification indicator plus the first letter of the triangle type is used for this modification. The modification is placed after the triangle symbol and the termination indicator signals an end to the modification.

# Triangle + Modification Indicator and letter + Termination Indicator

Acute Triangle | ⠫⠞ | ⠨⠁ | ⠻ |

Isosceles Triangle | ⠫⠞ | ⠨⠊ | ⠻ |

Obtuse Triangle | ⠫⠞ | ⠨⠕ | ⠻ |

Right Triangle | ⠫⠞ | ⠨⠗ | ⠻ |

Scalene Triangle | ⠫⠞ | ⠨⠎ | ⠻ |

# Examples:

$\mathrm{\u25fa}=\phantom{\rule{thickmathspace}{0ex}}\text{one}\phantom{\rule{thickmathspace}{0ex}}{90}^{\xb0}\text{angle}$⠸⠩⠀⠫⠞⠨⠗⠻⠀⠨⠅⠀⠠⠄⠐⠕⠀⠼⠔⠴⠘⠨⠡⠀⠁⠝⠛⠇⠑⠀⠸⠱

⠸⠩⠀⠫⠞⠨⠕⠻⠀⠸⠱⠀⠊⠎⠀⠁⠝⠀⠕⠃⠞⠥⠎⠑⠀⠞⠗⠊⠁⠝⠛⠇⠑⠲

# Modified Angles:

Like triangles, angles are often identified by their structure, such as right or acute, or obtuse.

Structural Shape Modification Indicator | ⠨ |

Termination Indicator | ⠻ |

A structural shape modification indicator plus the first letter of the angle type is used for this modification. The modification is placed after the angle symbol and the termination indicator signals an end to the modification.

# Angle + Modification Indicator and letter + Termination Indicator

Angle (non-descript) | ⠫⠪ | ||

Obtuse Angle | ⠫⠪ | ⠨⠕ | ⠻ |

Right Angle | ⠫⠪ | ⠨⠗ | ⠻ |

Straight Angle | ⠫⠪ | ⠨⠎ | ⠻ |

# Examples:

⠫⠪⠨⠎⠻⠀⠨⠅⠀⠼⠂⠦⠴⠘⠨⠡

$\mathrm{\u29a6}>{90}^{\xb0}$⠫⠪⠨⠕⠻⠀⠨⠂⠀⠼⠔⠴⠘⠨⠡

$\mathrm{\u299c}={90}^{\xb0}$⠫⠪⠨⠗⠻⠀⠨⠅⠀⠼⠔⠴⠘⠨⠡