This routine tests if the given triangle ABC is equilateral. It returns true if ABC is equilateral; false if it is not; and FAIL if it is unable to reach a conclusion.

In FAIL is returned, and the optional argument is given, then the condition that makes ABC equilateral is assigned to this argument. It will be either of the form $\mathrm{expr}=0$ or of the form $\&\mathrm{or}\left(\mathrm{expr\_1}=0,\mathrm{expr\_2}=0,...,\mathrm{expr\_n}\right)$ where expr, expri_i are maple expressions.

The command with(geometry,IsEquilateral) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{geometry}\right)\:$

$\mathrm{triangle}\left(\mathrm{ABC}\,\left[\mathrm{point}\left(A\,0\,0\right)\,\mathrm{point}\left(B\,2\,0\right)\,\mathrm{point}\left(C\,1\,2\right)\right]\right)$

$\mathrm{ABC}$

$\mathrm{IsEquilateral}\left(\mathrm{ABC}\right)$

$\mathrm{false}$

$\mathrm{point}\left(C\,1\,a\right)\:$

$\mathrm{IsEquilateral}\left(\mathrm{ABC}\,'\mathrm{cond}'\right)$

IsEquilateral:   "hint: one of the following conditions must be satisfied: {-a^2+3 = 0}"

$\mathrm{FAIL}$

$\mathrm{cond}$

$-a^2+3=0$

$\mathrm{assume}\left(\mathrm{cond}\right)$

$\mathrm{IsEquilateral}\left(\mathrm{ABC}\right)$

$\mathrm{true}$

$\mathrm{assume}\left(\mathrm{op}\left(1\,\mathrm{cond}\right)\ne \mathrm{op}\left(2\,\mathrm{cond}\right)\right)$

$\mathrm{IsEquilateral}\left(\mathrm{ABC}\right)$

$\mathrm{false}$

$\mathrm{assume}\left(0<a\right)$

$\mathrm{triangle}\left(T\&comma;\left[a\&comma;a\&comma;a\right]\right)$

$T$

$\mathrm{IsEquilateral}\left(T\right)$

$\mathrm{true}$