Question

which rule explains why these triangles are similar?

sss
sas
aa
none of the above; the triangles cannot be proven similar

Explanation:

Step1: Check SSS similarity

SSS similarity requires \(\frac{PQ}{GI}=\frac{QR}{IH}=\frac{PR}{GH}\).
\(\frac{65}{71}
eq\frac{55}{36}
eq\frac{30}{71}\), so SSS is not valid.

Step2: Check SAS similarity

SAS similarity requires two sides in proportion and included angle equal.
There is no information about angles, and \(\frac{PQ}{GI}
eq\frac{PR}{GH}\) (\(\frac{65}{71}
eq\frac{30}{71}\)), so SAS is not valid.

Step3: Check AA similarity

AA similarity requires two angles equal.
No angle information is given to prove two angles equal, so AA is not valid.

Answer:

none of the above; the triangles cannot be proven similar