## Shape

$90^{ \circ }$

90^{ \circ }

The small circle in the upper right corner representing degrees can be represented using \circ, which comes from "circle".

$\frac{ \pi }{ 2 }$

\frac{ \pi }{ 2 }

$\angle A$

\angle A

$AB /\!/ CD$

AB /\!/ CD

In Japan, two "/" signs are used to indicate parallelism. "\!" can be used to close the gap.

$AB \parallel CD$

AB \parallel CD

$AB \perp CD$

AB \perp CD

\perp comes from "perpendicular".

$\triangle ABC$

\triangle ABC

$\Box ABCD$

\Box ABCD

You can use \Box to represent a rectangle. It starts with a capital letter.

$\stackrel{\huge\frown}{AB}$

\stackrel{\huge\frown}{AB}

For arcs, since there is no proper command, we combine symbols. \forwn represents the arc symbol (looks like a frown mouth), and \huge makes it bigger. You can use \stackrel to stack the symbols on top of each other.

$\overparen{AB}$

\overparen{AB}

\overparen comes from "over" and "parentheses". It allows you to put round brackets over text. However, it don't display beautifully.

$\triangle ABC \equiv \triangle DEF$

\triangle ABC \equiv \triangle DEF

\equiv comes from "equivalent". In Japan, it is often written like this.

$\triangle ABC \cong \triangle DEF$

\triangle ABC \cong \triangle DEF

\cong comes from "congruent". This is the most common way to write globally.

$\triangle ABC \backsim \triangle DEF$

\triangle ABC \backsim \triangle DEF

The commonly used similarity symbol in Japan is obtained by rotating the letter S by 90 degrees. An equivalent symbol for this is "backsim." However, this symbol may feel a bit unfamiliar as it is a reversed tilde.

$\triangle ABC \sim \triangle DEF$

\triangle ABC \sim \triangle DEF

It is derived from the concept of similarity. It is more commonly used overseas to represent similarity.