Question

which rule explains why these scalene triangles are similar?
sss
sas
aa
none of the above; the triangles cannot be proven similar

Explanation:

Step1: Check the ratio of sides

First, calculate the ratios of the corresponding sides. For the sides \(45\) and \(63\), the ratio is \(\frac{45}{63}=\frac{5}{7}\). For the sides \(77\) and \(91\) (assuming a typo and it should be \(91\) as \(7\times13 = 91\) and \(77 = 7\times11\) is wrong, if we consider the other side \(35\) and \(49\) (typo assumed) \(\frac{35}{49}=\frac{5}{7}\)). But wait, let's check the angle - side relationship.

Step2: Analyze the given angle

We are given an angle of \(92^{\circ}\) in both triangles. For SAS (Side - Angle - Side) similarity, we need two pairs of sides in proportion and the included angle equal. \(\frac{45}{63}=\frac{5}{7}\), \(\frac{77}{107.8}\) (if following the ratio \(\frac{5}{7}\), \(77\times\frac{7}{5}=107.8\)) is wrong. Wait, no, actually \(\frac{45}{63}=\frac{5}{7}\), \(\frac{35}{49}=\frac{5}{7}\) (assuming \(77\) is a mis - print and should be \(49\)). And the included angle \(92^{\circ}\) is equal.

Answer:

SAS