Two triangular mirrors are similar. The first mirrors angels all measure 60 degrees. Wht are the measures of the second mirrors angles? Explain how you know.

Question

rebeccaxhawaii · Answer

it would be the same because mirror 1 is an equilateral triangle and all the angles must add up to 180 so 60+60+60=180 if mirror 2 were to be similar there would be no other choice than it being the exact same

rebeccaxhawaii · Answer

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mathstudent55 · Answer

@rebeccaxhawaii 
You are correct, but the question is simpler than you make it out to be.

The definition of similar polygons is:
Two polygons are similar if each pair of corresponding angles is congruent, and if the ratios of the lengths of all pairs of corresponding sides are equal.

In the case of similar triangle, because of AA similarity, if two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. In the case of similar triangles, you don't even need to look at the ratios of the lengths of the corresponding sides.

Now look at this problem.
From "Two triangular mirrors are similar." we know all angles of one triangle are congruent to all angles of the other triangle.
From "The first mirrors angles all measure 60 degrees." we can conclude that all angles of the second triangle also measure 60 degrees.

There is no need to add angles to get 180, or do any other work.