Question

the two polygons below are similar. complete the similarity statement. gh ij ~ save answer

Explanation:

Step1: Identify corresponding angles

In similar polygons, corresponding angles are equal. By observing the angle markings, we can match the angles of the two polygons.

Step2: Match the vertices in order

Starting with vertex \(G\) in the first polygon. The side \(GJ = 12\) and in the second polygon, the corresponding side (based on the ratio of sides \(\frac{12}{4}=3\), \(\frac{16}{6}=\frac{8}{3}\) (incorrect, actually looking at angle - side correspondence). Looking at the angle - side - angle structure:
The side \(GJ\) (length \(12\)) corresponds to \(TU\) (length \(4\)), \(GH\) (length \(16\)) corresponds to \(TS\) (length \(6\)) (no, actually, using the order of angles. The first polygon has vertices \(G\), \(H\), \(I\), \(J\).
In the second polygon, if we consider the angle - side - angle - side correspondence. The side \(GJ = 12\) and in the second polygon, the side \(VU=3\) (ratio \(\frac{12}{3} = 4\)), \(GH = 16\) and \(TV = 4\) (ratio \(\frac{16}{4}=4\)), \(HI=24\) and \(VS = 4\) (ratio \(\frac{24}{6}=4\) (no, wait, correct approach:
Since similar polygons have corresponding angles equal. The first polygon \(GHIJ\):

• \(\angle G\) corresponds to \(\angle T\)
• \(\angle H\) corresponds to \(\angle S\)
• \(\angle I\) corresponds to \(\angle V\)
• \(\angle J\) corresponds to \(\angle U\)

Answer:

\(GHIJ\sim TSVU\)