In square ABCD, M is the middle point of AB side, take a point E on ad to make AE = 1 / 4AD (1) Please judge the position relationship between me and MC and explain the reason. (2) if the area of this square is 64, find the length of EC (to use Pythagorean theorem)

In square ABCD, M is the middle point of AB side, take a point E on ad to make AE = 1 / 4AD (1) Please judge the position relationship between me and MC and explain the reason. (2) if the area of this square is 64, find the length of EC (to use Pythagorean theorem)

1）
In right triangle ame and right triangle BCM
AE/BM=AM/BC=1/2

As shown in the figure, take a point E on one side ad of the square ABCD, make AE = 1 / 4AD, make OK through the midpoint o of AB, perpendicular to EC and K, try to explain: the square of OK = EK × KC

As shown in the figure, ∵ AE = 1 / 4AD, Ao = 1 / 2Ab, ∵ AE: Ao = 1:2
Moreover, OB: BC = 1:2, and the triangular AEO is similar to OBC
■ ∠ AOC = 90 ° AOK + ∠ Koc = 90 ° C
The ADK is similar to Koc
∴OK/EK=KC/OK
That is, the square of OK = EK × KC

As shown in the figure, in ladder ABCD, ad ‖ BC, point E is on BC, AE = be, and AF ⊥ AB, connect EF. (1) if EF ⊥ AF, AF = 4, ab = 6, find the length of & nbsp; AE. (2) if point F is the midpoint of CD, prove: CE = be-ad

(1) Let em ⊥ AB intersect AB at points M. ∵ AE = be, EM ⊥ AB, ∵ am = BM = 12 × 6 = 3; ∵ EF ⊥ AF, ∵ ame = {MAF =} AFE = 90 °, ∵ quadrilateral amef is rectangle, ∵ EF = am = 3; in RT △ AFE, AE = af2 + ef2 = 5; (2) extend the intersection of AF and BC at points n. ∵ ad ∥ en, ∵ DAF =} n

In the square ABCD with side length of 1, AC is diagonal, AE bisects ∠ DAC, EF ⊥ AC, f is perpendicular, and the length of FC and EC is calculated
In half an hour ~ FZ will not talk

You give more branches!
According to Pythagorean theorem, AC = √ 2
Because EF ⊥ AC, ∠ d = ∠ EFA = 90 degrees
And AE is equal to ∠ DAC, so ∠ DAE = ∠ FAE
Again AE = AE
So △ AFE ≌ △ ade
So ad = AF = 1
So FC = ac-af = √ 2-1
Because ∠ ACD = 45
And ∠ EFC = 90
So the triangle EFC is an isosceles right triangle
With Pythagorean theorem, we can get EC = 2 - √ 2