Respuesta :
An equilateral triangle with side length 6 is similar to an equilateral triangle with side length 15
Solution:
Given that we have to find whether the polygons are similar
An equilateral triangle with side length 6
An equilateral triangle is a triangle in which all three sides are equal
All three internal angles are also congruent to each other and are each 60°
Let ABC be a equilateral triangle with side length 6
Since all three sides are equal,
AB = 6
BC = 6
CA = 6
Also, angle A = 60 degrees and angle B = 60 degrees and angle C = 60 degrees
An equilateral triangle with side length 15
Let XYZ be a equilateral triangle with side length 15
Since all three sides are equal in equilateral triangle,
XY = 15
YZ = 15
ZX = 15
Also, angle X = 60 degrees and angle Y = 60 degrees and angle Z = 60 degrees
Two triangles are similar if they have the same angles and the side lengths are proportional.
Since,
[tex]\frac{AB}{XY} = \frac{BC}{YZ} = \frac{CA}{ZX} = \frac{6}{15} = \frac{2}{5}[/tex]
Also,
Angle A = angle X = 60 degrees
Angle B = angle Y = 60 degrees
Angle C = angle Z = 60 degrees
Since equilateral triangles all have the same angles, and all side lengths are equal, any two equilateral triangles must be similar.
