Question

show or explain how you know. figures of quadrilaterals efgh (sides: ef=3, fg=3.6, gh=3, he=3.6; angles: ∠e=85°, ∠f=95°, ∠g=85°, ∠h=95°) and abcd (sides: ab=2, bc=2.4, cd=2, da=2.4; angles: ∠a=85°, ∠b=95°, ∠c=85°, ∠d=95°). options: “similar” (selected) or “not similar”

Explanation:

Step1: Check angle correspondence

Both quadrilaterals have angles \(85^\circ\) and \(95^\circ\) in the same order, so corresponding angles are equal.

Step2: Check side ratios

For the first quadrilateral (EFGH): side lengths are \(3\) (EF, GH) and \(3.6\) (FG, EH).
For the second quadrilateral (ABCD): side lengths are \(2\) (AB, CD) and \(2.4\) (BC, AD).
Calculate ratios: \(\frac{3}{2} = 1.5\) and \(\frac{3.6}{2.4} = 1.5\). So corresponding sides are proportional.

Step3: Apply similarity criteria

Since corresponding angles are equal and corresponding sides are proportional, the quadrilaterals are similar by the definition of similar polygons.

Answer:

The quadrilaterals are similar because corresponding angles are equal (\(85^\circ\) and \(95^\circ\) match) and corresponding sides are proportional (\(\frac{3}{2}=\frac{3.6}{2.4} = 1.5\)).