Question

a. are any two equilateral triangles always similar? yes no

Explanation:

Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion. For any two equilateral triangles, all angles are \(60^{\circ}\) (so corresponding angles are equal). Also, if the side lengths of one equilateral triangle are \(a,b,c\) (where \(a = b=c\)) and of another are \(A,B,C\) (where \(A = B=C\)), then \(\frac{a}{A}=\frac{b}{B}=\frac{c}{C}\) (since \(a = b=c\) and \(A = B=C\)).

Answer:

Yes