1. (2023·靖江月考)根据下列条件能画出唯一$\triangle ABC$的是 ()
A. $AB = 2$,$BC = 6$,$AC = 9$
B. $AB = 7$,$BC = 5$,$\angle A = 30^{\circ}$
C. $\angle A = 50^{\circ}$,$\angle B = 60^{\circ}$,$\angle C = 70^{\circ}$
D. $AC = 3.5$,$BC = 4.8$,$\angle C = 70^{\circ}$

2. (2024·镇江期末)如图,$\triangle ABC\cong \triangle DEC$,点$E$在线段$AB$上,$\angle B = 70^{\circ}$,则$\angle ACD$的度数为 ()

A. $20^{\circ}$
B. $30^{\circ}$
C. $40^{\circ}$
D. $50^{\circ}$

3. (2023·丽水)如图,在$\triangle ABC$中,$AC$的垂直平分线交$BC$于点$D$,交$AC$于点$E$,$AB = AD$.若$AB = 4$,则$DC$的长是 ()

A. 2
B. 4
C. 6
D. 8

4. 如图,$AD$是$\triangle ABC$的角平分线,$DE\perp AB$于点$E$,$S_{\triangle ABC} = 10$,$DE = 2$,$AB = 4$,则$AC$的长是 ()

A. 9
B. 8
C. 7
D. 6

5. 如图,已知点$B$,$E$,$F$,$C$在同一直线上,$BE = CF$,$AF = DE$,则添加条件,可以判定$\triangle ABF\cong \triangle DCE$.

6. 如图,在$\triangle ABC$中,$AD\perp BC$,$CE\perp AB$,垂足分别为$D$,$E$,$AD$,$CE$交于点$H$,已知$EH = EB = 3$,$AE = 4$,则$CH$的长是______.

7. 如图,在$\triangle ABC$中,$\angle C = 90^{\circ}$,$AD$平分$\angle CAB$交$BC$于点$D$,若$BD:DC = 2:1$,$BC = 15\mathrm{cm}$,则点$D$到$AB$的距离为$\mathrm{cm}$.