Question

similar polygons
in problems 1-2, determine if the two polygons are similar. if they are similar, write a similarity statement and the scale factor.
1)
two pentagons: left labeled a, b, c, d, e with side lengths ab=4, bc=4, cd=6, de=2, ea=6; right labeled w, x, y, z, v with side lengths wx=5, xy=5, yz=7.5, zv=2.5, vw=7.5

Explanation:

Step1: Check Corresponding Sides Ratio

First, identify corresponding sides. For the pentagons, we match sides: \(AB = 4\), \(BC = 4\), \(CD = 6\), \(DE = 2\), \(EA = 6\) (left pentagon); \(WX = 5\), \(XY = 5\), \(YZ = 7.5\), \(ZV = 2.5\), \(VW = 7.5\) (right pentagon). Calculate ratios:
\(\frac{AB}{WX}=\frac{4}{5}\), \(\frac{BC}{XY}=\frac{4}{5}\), \(\frac{CD}{YZ}=\frac{6}{7.5}=\frac{4}{5}\), \(\frac{DE}{ZV}=\frac{2}{2.5}=\frac{4}{5}\), \(\frac{EA}{VW}=\frac{6}{7.5}=\frac{4}{5}\). All ratios are equal.

Step2: Check Angles (Regular Pentagon)

Both are regular pentagons, so all interior angles are equal (\(108^\circ\)). Similarity requires equal angles and proportional sides.

Answer:

The pentagons \(ABCDE\) and \(WXYZV\) are similar. Similarity statement: \(ABCDE \sim WXYZV\). Scale factor: \(\frac{4}{5}\) (from \(ABCDE\) to \(WXYZV\)) or \(\frac{5}{4}\) (reverse).