The two symbols have slightly different shapes, but we can resize the black triangle to fit.
\documentclass{article}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage{color}
\makeatletter
\newcommand{\btriangle}{\mathpalette\btriangle@\relax}
\newcommand{\btriangle@}[2]{%
\begingroup
\sbox\z@{$\m@th#1\triangle$}%
\makebox[\wd\z@]{%
\raisebox{0.04\height}{%
\resizebox{1.1\wd\z@}{0.96\ht\z@}{%
$\m@th#1\blacktriangle$%
}%
}%
}%
\endgroup
}
\makeatother
\begin{document}
$\triangle\btriangle\blacktriangle$
\textcolor{red}{$\btriangle$}\llap{$\triangle$}
\textcolor{red}{$\triangle$}\llap{$\btriangle$}
$\scriptstyle\triangle\btriangle$
\textcolor{red}{$\scriptstyle\btriangle$}\llap{$\scriptstyle\triangle$}
\textcolor{red}{$\scriptstyle\triangle$}\llap{$\scriptstyle\btriangle$}
\end{document}
The color
package is only needed for the examples of superposition that show the greater similarity of the symbols we get.

\vartriangle
from amsmath)?