Problem
GEO-B1-M03-P007 Similarity by Two Sides and an Angle
#7
★★☆☆☆ Level 2 of 5
In triangles \(ABC\) and \(DEF\), it is known that \(\angle A=\angle D\), \(AB=6\), \(AC=10\), \(DE=9\), \(DF=15\). Prove that the triangles are similar.
Compare the ratios of the sides containing the equal angles.
We have \(\frac{AB}{DE}=\frac{6}{9}=\frac{2}{3}\) and \(\frac{AC}{DF}=\frac{10}{15}=\frac{2}{3}\). The included angles are equal. Hence the triangles are similar by SAS.
Good for distinguishing SAS similarity from SAS congruence.