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# Lesson 10.1: Sings of Comparison: Approximately Equal To, Similar To, Congruent To

## Approximately equals sign

When comparing quantities, the values may be nearly equal, but are not exactly equal or identical. Since it would be erroneous to show the comparison with the parallel lines of an equals sign, the print symbol for approximately equals consists of parallel wavy lines, double tilde. The braille symbol for approximately equals, dot four dots one five six dot four dots one five six, resembles its print equivalent. It uses the symbol for tilde, but in a vertical rather than horizontal configuration.

≈ approximately equal to

## Similar to sign, tilde

If the measures of respective angles are equal and the measures of respective sides are in the same proportion, then geometric figures are considered to be mathematically similar. The print symbol for similar to consists of a single wavy line, tilde. The braille symbol for similar to is dot four dots one five six.

∼ similar to

## Congruent to sign

When two figures are similar and the measures of their respective sides are equal, then the figures are considered to be congruent. Both the print and braille symbols combine the symbol for similarity with the symbol for equality. In print, the tilde appears above the equals sign. The braille sign for congruent to is dot four dots one five six dots four six dots one three.

≅ congruent to

### Example 1

$1.78\approx 1.8$
⠼⠂⠨⠶⠦⠀⠈⠱⠈⠱⠀⠼⠂⠨⠦

### Example 2

$\pi \approx 3.14$
⠨⠏⠀⠈⠱⠈⠱⠀⠼⠒⠨⠂⠲

### Example 3

$△ABC\sim △XYZ$
⠫⠞⠀⠠⠁⠠⠃⠠⠉⠀⠈⠱⠀⠫⠞⠀⠠⠭⠠⠽⠠⠵

### Example 4

$\text{trapezoid}\phantom{\rule{.3em}{0ex}}ABCD\sim \text{trapezoid}\phantom{\rule{.3em}{0ex}}MNOP$
⠫⠵⠀⠠⠁⠠⠃⠠⠉⠠⠙⠀⠈⠱⠀⠫⠵⠀⠠⠍⠠⠝⠠⠕⠠⠏

### Example 5

$△ABC\cong △XYZ$
⠫⠞⠀⠠⠁⠠⠃⠠⠉⠀⠈⠱⠨⠅⠀⠫⠞⠀⠠⠭⠠⠽⠠⠵

### Example 6

$\stackrel{‾}{\mathrm{AB}}\cong \stackrel{‾}{\mathrm{CD}}$
⠐⠠⠁⠠⠃⠣⠱⠻⠀⠈⠱⠨⠅⠀⠐⠠⠉⠠⠙⠣⠱⠻

### Example 7

$\angle A\cong \angle B$
⠫⠪⠀⠠⠁⠀⠈⠱⠨⠅⠀⠫⠪⠀⠠⠃