geometry - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Geometry : 2-D Euclidean : Triangle Geometry : geometry/AreSimilar

geometry

  

AreSimilar

  

test if two triangles are similar

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

AreSimilar(T1, T2, cond)

Parameters

T1, T2

-

two triangles

cond

-

(optional) name

Description

• 

Two similar triangles T1 and T2 are triangles whose corresponding angles are congruent and whose corresponding sides are in proportion.

• 

The routine returns true if T1 and T2 are similar; false if they are not; and FAIL if it is unable to reach a conclusion.

• 

In FAIL is returned, and the optional argument is given, the condition that makes T1 and T2 similar is assigned to this argument. It will be either of the form expr=0 or of the form &orexpr_1=0,...,expr_n=0 where expr, expr_i are Maple expressions.

• 

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

Examples

withgeometry:

pointA,0,0,pointB,0,3,pointC,1,0,pointH,0,6,pointF,2,0:

pointG,3,1:

triangleT1,A,B,C:

triangleT2,A,H,F:

triangleT3,A,H,G:

AreSimilarT1,T2

true

(1)

AreSimilarT1,T3

false

(2)

pointH,0,Hy,pointG,Gx,1:

AreSimilarT1,T3,'cond'

AreSimilar:   "hint: one of the following conditions must be satisfied: {{9/Hy^2-10/(Gx^2+(Hy-1)^2) = 0, 9/Hy^2-1/(Gx^2+1) = 0}, {9/Hy^2-1/(Gx^2+(Hy-1)^2) = 0, 9/Hy^2-10/(Gx^2+1) = 0}, {9/(Gx^2+(Hy-1)^2)-10/Hy^2 = 0, 9/(Gx^2+(Hy-1)^2)-1/(Gx^2+1) = 0}, {9/(Gx^2+(Hy-1)^2)-1/Hy^2 = 0, 9/(Gx^2+(Hy-1)^2)-10/(Gx^2+1) = 0}, {9/(Gx^2+1)-10/Hy^2 = 0, 9/(Gx^2+1)-1/(Gx^2+(Hy-1)^2) = 0}, {9/(Gx^2+1)-1/Hy^2 = 0, 9/(Gx^2+1)-10/(Gx^2+(Hy-1)^2) = 0}}"

FAIL

(3)

cond

9Hy210Gx2+Hy12=0,9Hy21Gx2+1=09Hy21Gx2+Hy12=0,9Hy210Gx2+1=09Gx2+Hy1210Hy2=0,9Gx2+Hy121Gx2+1=09Gx2+Hy121Hy2=0,9Gx2+Hy1210Gx2+1=09Gx2+110Hy2=0,9Gx2+11Gx2+Hy12=09Gx2+11Hy2=0,9Gx2+110Gx2+Hy12=0

(4)

Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam