Question

1. which of the following additional statements would you need to prove these two triangles are similar by sas similarity?

∠c ≅ ∠f
∠b ≅ ∠e
∠a ≅ ∠d

Explanation:

Step1: Recall SAS similarity criterion

SAS (Side - Angle - Side) similarity states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the two triangles are similar.
For \(\triangle ABC\) and \(\triangle DEF\), we have \(\frac{AB}{DE}=\frac{7}{14}=\frac{1}{2}\) and \(\frac{AC}{DF}=\frac{12}{24}=\frac{1}{2}\).

Step2: Identify the included angles

The included angles for the sides \(AB, AC\) in \(\triangle ABC\) is \(\angle A\), and for the sides \(DE, DF\) in \(\triangle DEF\) is \(\angle D\).

Answer:

\(\angle A\cong\angle D\)