Two. In a regular pentagon, Mn = NP = PQ = QD = DM = M, AD = BC = C'd = B, AB = CD = A.
∠DMN =∠MNP =∠NPQ =∠PQD =∠QDM = 108
① From the folding process, DE=BE, ∠ ADE = ∠ CDF = ∠ QDM-∠ ADC =108-90 =18.
There is AE/AD=tan∠ADE in Rt△ADE, that is, AE = ad * tan ∠ ade = b * tan 18.
Answer? -B? =(AE+EB)? -Advertising?
=(AE+ED)? -Advertising?
=AE? +2AE*ED+ED? -Advertising?
=2AE? +2AE*ED
=2AE(AE+ED)
=2AE(AE+EB)
=2*b tan 18 *a
=2ab tan 18
② If DN is connected, then ∠ NDG = ∠ MDG-∠ MDN = ∠ QDM/2-(180-∠ DMN)/2 =18.
GN = NP/2 = m/2,DG = BG = BD/2 = √(a? +b? )/2
In Rt△DNG, tan ∠ ndg = ng/DG = (NP/2)/(BD/2) = NP/BD.
That is, m = NP = BD tan∠NDG = √(a? +b? )tan 18
3 even billions.
AE and A'E' are symmetrical about MN, AE intersects with A'E' at point B, so B is on the symmetry axis MN, that is, the BMN*** line.
In Rt△ABM, ∠ ABM = 90-∠ AMB = 90-(180-108) =18.
tan∠ABM = AM/AB = (AD-DM)/AB
b = AD
= DM + AB tan∠ABM
= m + a tan 18
④ If NH⊥MQ is in H, then ∠ MNH = ∠ MNP-∠ PNH =108-90 =18.
In Rt△MNH, tan∠MNH = MH/NH.
A'H = NG = NP/2 = m/2
There is MH = mnsin ∠ mnh = msin 18.
b = AD
= DM + AM
= Deutsche Mark+AM
= DM + A'H + MH
= m + m/2 + m sin 18
= (3/2)m + m sin 18
& lt(3/2)m + m tan 18
Therefore, ① ② ③ holds, ④ does not.