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geometry

  

IsEquilateral

  

test if a given triangle is equilateral

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

IsEquilateral(ABC, cond)

Parameters

ABC

-

triangle

cond

-

(optional) name

Description

• 

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 expr=0 or of the form &orexpr_1=0,expr_2=0,...,expr_n where expr, expri_i are maple expressions.

• 

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

Examples

withgeometry:

triangleABC,pointA,0,0,pointB,2,0,pointC,1,2

ABC

(1)

IsEquilateralABC

false

(2)

pointC,1,a:

IsEquilateralABC,'cond'

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

FAIL

(3)

cond

a2+3=0

(4)

assumecond

IsEquilateralABC

true

(5)

assumeop1,condop2,cond

IsEquilateralABC

false

(6)

assume0<a

triangleT&comma;a&comma;a&comma;a

T

(7)

IsEquilateralT

true

(8)

See Also

geometry[IsRightTriangle]

geometry[triangle]

 


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