Question

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

Explanation:

Step1: Calculate the ratios of corresponding sides

For \(\triangle TSU\) and \(\triangle JHI\):

• \(\frac{TS}{JH}=\frac{32}{72}=\frac{4}{9}\)
• \(\frac{SU}{HI}=\frac{40}{48}=\frac{5}{6}\)
• \(\frac{UT}{IJ}=\frac{48}{60}=\frac{4}{5}\)

Since \(\frac{32}{72}
eq\frac{40}{48}
eq\frac{48}{60}\), the SSS (Side - Side - Side) similarity rule (which requires \(\frac{a}{a'}=\frac{b}{b'}=\frac{c}{c'}\) for corresponding sides \(a,a'\), \(b,b'\), \(c,c'\) of two triangles) does not apply.

There is no information about included angles to check the SAS (Side - Angle - Side) similarity rule (which requires \(\frac{a}{a'}=\frac{b}{b'}\) and the included angles to be equal). And no information about two pairs of equal angles to check the AA (Angle - Angle) similarity rule.

Answer:

none of the above; the triangles cannot be proven similar