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# Lesson 8.1: Signs of Comparison: approximately equal to, similar to, congruent to

## Symbols

$\approx \phantom{\rule{.3em}{0ex}}\text{approximately equal to}$
⠘⠔

$\sim \phantom{\rule{.3em}{0ex}}\text{similar to}$
⠈⠔

$\cong \phantom{\rule{.3em}{0ex}}\text{congruent to}$
⠐⠸⠔

## Review

A blank space is left before and after a sign of comparison. Numeric mode is terminated by a space. The numeric indicator is required before the numeral that follows a sign of comparison.

Complex algebraic equations are best enclosed in grade 1 passage indicators to ensure that letters standing alone and indicators such as superscript, subscript, fractions, radicals, arrows and shapes are well defined without the need for grade 1 symbol indicators.

The angle symbol is not considered a shape. Follow print for use and spacing of the angle symbol.

## Explanation

When values are compared, they may be nearly equal but are not exactly equal or identical. Quantities are denoted as approximately equal to by the print symbol of a double tilde or two parallel wavy lines. The braille symbol for approximately equal to is made with two cells; dots four five in the first cell and dots three five in the second cell.

Geometric figures are considered to be mathematically similar when the measures of respective angles are equal and the measures of respective sides are in the same proportion. The print symbol used to denote similar to is a tilde (single wavy line). In braille, the tilde symbol is formed with two cells: dot four in the first cell and dots three five in the second cell.

Congruent means exactly equal in size and shape. In mathematics, line segments, angles, triangles, and other figures can be congruent. The symbol for congruent is a tilde above the equals sign. In braille, the congruent to symbol is three cells: dot five in the first cell, dots four five six in the second cell and dots three five in the third cell.

### Example 1

$2.78\approx 2.8$
⠼⠃⠲⠛⠓⠀⠘⠔⠀⠼⠃⠲⠓

### Example 2

$\pi \approx 3.14$
⠨⠏⠀⠘⠔⠀⠼⠉⠲⠁⠙

### Example 3

$△\phantom{\rule{.3em}{0ex}}\mathrm{ABC}\sim △\phantom{\rule{.3em}{0ex}}\mathrm{DEF}$
⠰⠰⠰⠫⠼⠉⠀⠠⠠⠁⠃⠉⠀⠈⠔⠀⠫⠼⠉⠀⠠⠠⠙⠑⠋⠰⠄

### Example 4

$▱\phantom{\rule{.3em}{0ex}}\mathrm{ABCD}\sim ▱\phantom{\rule{.3em}{0ex}}\mathrm{MNOP}$
⠰⠰⠰⠫⠈⠼⠙⠀⠠⠠⠁⠃⠉⠙⠀⠈⠔⠀⠫⠈⠼⠙⠀⠠⠠⠍⠝⠕⠏⠰⠄

### Example 5

$△\phantom{\rule{.3em}{0ex}}\mathrm{ABC}\cong △\phantom{\rule{.3em}{0ex}}\mathrm{DEF}$
⠰⠰⠰⠫⠼⠉⠀⠠⠠⠁⠃⠉⠀⠐⠸⠔⠀⠫⠼⠉⠀⠠⠠⠙⠑⠋⠰⠄

### Example 6

$\stackrel{‾}{\mathrm{MN}}\cong \stackrel{‾}{\mathrm{OP}}$
⠰⠰⠰⠣⠠⠠⠍⠝⠜⠱⠀⠐⠸⠔⠀⠣⠠⠠⠕⠏⠜⠱⠰⠄

### Example 7

$\angle C\cong \angle D$
⠸⠪⠠⠉⠀⠐⠸⠔⠀⠸⠪⠠⠙

In Example 8, the upper case letters ABC on the right side of the expression are each followed by the prime symbol. The capital word indicator is not used because its effect is terminated by a non-alphabetic character, in this case the prime symbol.

### Example 8

$△\mathrm{ABC}\sim △{A}^{\prime }{B}^{\prime }{C}^{\prime }$
⠰⠰⠰⠫⠼⠉⠱⠠⠠⠁⠃⠉⠀⠈⠔⠀⠫⠼⠉⠱⠠⠁⠶⠠⠃⠶⠠⠉⠶⠰⠄