In the trapezoidal ABCD, ab ‖ CD, ∠ a = 90 °, ab = 2, BC = 3, CD = 1, e is the midpoint of AD. try to judge the position relationship between EC and EB, and write the inference

In the trapezoidal ABCD, ab ‖ CD, ∠ a = 90 °, ab = 2, BC = 3, CD = 1, e is the midpoint of AD. try to judge the position relationship between EC and EB, and write the inference

CF ⊥ AB is made through point C, and F is perpendicular to the foot
Then AF = BF = 1, ∠ a = 90 °
Then ∠ f = 90 ° CF = √ (BC & sup2; - BF & sup2;) = 2 √ 2
Then AE = de = √ 2
Then CE = √ (de & sup2; + DC & sup2;) = √ 3, be = √ (AB & sup2; + AE & sup2;) = √ 6
Then BC & sup2; = 9, CE & sup2; + be & sup2; = 3 + 6 = 9
∴BC²=BE²+CE²
That is, CEB = 90 degree
EC ⊥ EB