Question

determine if \\( \triangle g h f \\) is similar to \\( \triangle a b c \\). if they are similar, enter the scale factor from \\( \triangle a b c \\) to \\( \triangle g h f \\). if they are not similar, enter none.

\\( m \angle g = m \angle a = 43 ^ { \circ } \\)

Explanation:

Step1: Check the ratio of corresponding sides

For \(\triangle ABC\) and \(\triangle GHF\), we have two pairs of corresponding sides. Let's find the ratios.
The ratio of \(AB\) to \(GH\) is \(\frac{AB}{GH}=\frac{9}{12}=\frac{3}{4}\).
The ratio of \(AC\) to \(GF\) is \(\frac{AC}{GF}=\frac{10}{16}=\frac{5}{8}\).
Since \(\frac{3}{4}
eq\frac{5}{8}\), the triangles are not similar by the Side - Angle - Side (SAS) similarity criterion (because the included angles \(\angle A=\angle G = 43^{\circ}\), but the ratios of the adjacent sides are not equal).

Answer:

None