CD = CE = DE = 2cm
△ CDE is an equilateral triangle.
∴∠CDE=∠DCE=∠DEC=60
∴∠adg=360-∠ADC-∠gde-∠CDE = 360-90-90-60 = 120
∴∠day=( 180- 120)× 1/2 = 30
∴dy= 1/2ad= 1/2× 1=0.5(cm)
That is, the distance from point d to AG is 0.5cm.
②? ∵α=45
∴∠NCE=∠NEC=45
∴∠CNE=90 ∴∠HND=∠CNE=90
∴∠HND=∠D=∠H=90
∴ Quadrilateral HNDM is a rectangle (a quadrilateral with three right angles is a rectangle)
CD = EH (known) CN=EN (confirmed)
∴CD-CN=EH-EN, that is, HN=DN.
∴ Quadrilateral HNDM is a rectangle (a group of rectangles with equal adjacent sides is a square)
Also, there is a small mistake in the above picture: