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.