Symbol for Filled Triangle

Question

\blacktriangle gives a filled triangle symbol, but it is slightly smaller than \triangle. Is there a command that gives a filled triangle symbol whose size is exactly equal to \triangle?

If I have no choice but to use a package (other than ams packages), then could you recommand a package that does not change any other symbols and enables me to extract only that symbol?

Thank you.

Answer 1

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.