Question

An equilateral triangle with side length 6 and an equilateral triangle with side length 15 determine whether the polygons are similar

Answer 1

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,

$\frac{AB}{XY} = \frac{BC}{YZ} = \frac{CA}{ZX} = \frac{6}{15} = \frac{2}{5}$

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.