It is known that: as shown in the figure, ∠ B = ∠ C = 90 °, M is the midpoint of BC, DM bisects ∠ ADC. (1) prove that am bisects ∠ bad; (2) try to explain the position relationship between DM and am? (3) What is the relationship between CD, AB and ad? Write the results directly

It is known that: as shown in the figure, ∠ B = ∠ C = 90 °, M is the midpoint of BC, DM bisects ∠ ADC. (1) prove that am bisects ∠ bad; (2) try to explain the position relationship between DM and am? (3) What is the relationship between CD, AB and ad? Write the results directly

(1) It is proved that me ⊥ ad is made in E, ∵ MC ⊥ DC, me ⊥ Da, MD bisection ⊥ ADC, ∵ me = MC, ∵ me = MC, ∵ me = MB, me ⊥ ad, MB ⊥ AB, ∵ am bisection ⊥ DAB. (2) DM ⊥ am, the reason is that ∵ DM bisection ⊥ CDA, am bisection ⊥ DAB, ∵ 1 = ∧ 2, ∧ 3 = ∧ 4, ∫ DC ∥ AB, ∧ CDA + ∧ bad = 180 °, ∧ 1 + ∧ 3 = 90 ° and ∧ DMA = 180 The reason is: DM ⊥ am. (3) CD + AB = ad, the reason is: me ⊥ ad, MC ⊥ CD, C = DEM = 90 ° in RT △ DCM and RT △ DEM, DM = DMEM = cm ⊥ RT △ DCM ≌ RT △ DEM (HL), ≌ CD = De, AE = AB, ≂ AE + de = ad, ≌ CD + AB = ad