The polygons have congruent angles (∠ABC = ∠FGH = 103°, ∠BCD = ∠GHE = 84°) but not all corresponding sides are proportional (AB/FG ≠ BC/GH ≠ CD/HE ≠ DA/EF), indicating they are not similar.
Given:
Angles:
∠ABC = ∠FGH = 103°
∠BCD = ∠GHE = 84°
We need to find:
∠DAB and ∠FEH
Finding ∠DAB
The sum of interior angles in a quadrilateral is 360°.
∠DAB = 360° - (∠ABC + ∠BCD + ∠CDA)
∠DAB = 360° - (103° + 84° + 95°)
∠DAB = 360° - 282°
∠DAB = 78°
Finding ∠FEH
Using the same logic:
∠FEH = 360° - (∠FGH + ∠GHE + ∠HEF)
∠FEH = 360° - (103° + 84° + 95°)
∠FEH = 360° - 282°
∠FEH = 78°
Therefore, both ∠DAB and ∠FEH are 78°.
Now, let's move on to the side lengths to check for proportionality.
Given side lengths:
AB = 2014, BC = 1611, CD = 2014, DA = 1861
Checking for side length proportionality
For two polygons to be similar, their corresponding sides must be in proportion.
AB/FG = BC/GH = CD/HE = DA/EF
AB/FG = 2014/107 = 18.79
BC/GH = 1611/84 = 19.18
CD/HE = 2014/107 = 18.79
DA/EF = 1861/936.5 = 1.99
Since not all corresponding sides have the same ratio, the polygons are not similar.
Therefore, after analyzing both angles and side lengths, the conclusion remains: the two polygons are not similar.
complete the question
Verifying Whether Two Given Polygons Are Similar
Are the two polygons similar?