Problem
GEO-B1-M03-P001 Two Equal Angles
#1
★☆☆☆☆ Level 1 of 5
In triangles \(ABC\) and \(DEF\), \(\angle A=\angle D\), \(\angle B=\angle E\), \(AB=5\), \(DE=15\), and \(BC=7\). Find \(EF\).
The triangles are similar by two angles. Find the similarity ratio.
By AA, \(\triangle ABC\sim\triangle DEF\). Side \(AB\) corresponds to \(DE\), so the ratio is \(\frac{15}{5}=3\). Side \(BC\) corresponds to \(EF\), hence \(EF=7\cdot3=21\).
Checks the most basic use of AA and side correspondence.