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In known trapezoid ABCD, AD / / BC, ∠ B = 90 degrees, ad = 3, BC = 5, ab = 1, rotate the line CD 90 degrees counterclockwise around point d to D and 90 degrees counterclockwise to de position What is the length of AE if AE is connected?
Make vertical lines of AD and BC respectively through E and D. EF intersects ad at F, DG intersects BC at G
&It is easy to prove that triangle def and triangle DCG are congruent
&There are DF = DG = AB = 1, EF = CG = BC-AD = 2
&In the right triangle AEF, AE = √ 4 ^ 2 + 2 ^ 2 = 2 √ 5
In known trapezoid ABCD, ad is parallel to BC, angle B = 90 degrees, ad = 3, BC = 5, ab = 1. Rotate the segment CD 90 degrees counterclockwise around point d to the de position, and connect AE
What is the length of AE?
Make ef perpendicular to ad through point E, and make the extension line of ad at point F
Easy to get EF = 5-3 = 2
DF=AB=1
So AF = 4
So AE = 2 times root 5
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