Which set of shapes contains members that are always similar to one another?

Question

anonymous · Answer

trapezoids
isosceles triangles
equilateral triangles
rectangles
pentagons

mathstudent55 · Answer

Use the angles.
If two polygons are similar, then all the pairs of corresponding angles are congruent.

mathstudent55 · Answer

Here are two trapezoids. They are drawn to scale.
Are all pairs of corresponding angles congruent?
|dw:1435246347755:dw|

anonymous · Answer

so it trapezoid

mathstudent55 · Answer

No. Just answer my question above for the trapezoids I drew.

mathstudent55 · Answer

When two polygons are similar, you can enlarge or reduce one of them to fit exactly on top of the the one. Do these two trapezoids look like with an enlargement or reduction on one of them, one would fit exactly on top of the other one?

anonymous · Answer

no

anonymous · Answer

so whats the answer

anonymous · Answer

Equilateral triangles.

mathstudent55 · Answer

Right. That means my drawing shows an example of two trapezoids that are NOT similar.
In other words, not all trapezoids are similar.

anonymous · Answer

thank you

mathstudent55 · Answer

Now let's move on to isosceles triangles.
|dw:1435246772609:dw|
The two triangles are isosceles, but not similar.

mathstudent55 · Answer

All equilateral triangles are similar.

mathstudent55 · Answer

|dw:1435246848604:dw|