Question

which rule explains why these scalene triangles are similar? t u 30 94° j 43 48 94° h 34 i s sss sas aa none of the above; the triangles cannot be proven similar

Explanation:

To determine triangle similarity, we check the rules:

• SSS Similarity: Requires all three corresponding sides to be in proportion. For $\triangle TUS$ and $\triangle JHI$, the sides are $30, 48$ (and unknown) vs. $34, 43$ (and unknown). Calculating ratios: $\frac{30}{34}\approx0.882$, $\frac{48}{43}\approx1.116$. These ratios are not equal, so SSS fails.
• SAS Similarity: Requires two sides in proportion and the included angle equal. The included angle for the sides we have ($30, 48$ in $\triangle TUS$; $34, 43$ in $\triangle JHI$) is $94^\circ$ in both, but the side ratios are not equal (as shown above), so SAS fails.
• AA Similarity: Requires two corresponding angles equal. We only know one angle ($94^\circ$) is equal; no other angle info is given, so AA fails.

Since none of SSS, SAS, or AA apply, the triangles cannot be proven similar.

Answer:

none of the above; the triangles cannot be proven similar