17.如图15,在三角形ABC中,点D,F在边BC上,点E在边AB上,点G在边AC上,EF与GD的延长线交于点H,∠1=∠B,∠2+∠3=180°.
(1)判断EH与AD的位置关系,并说明理由;
(2)若∠DGC=58°,且∠H=∠4+10°,求∠H的度数.

17. (1)$EH// AD$,理由如下：
$\because ∠1=∠B,\therefore AB// GD$,
$\therefore ∠2=∠BAD$.
$\because ∠2+∠3=180°$,
$\therefore ∠BAD+∠3=180°$,
$\therefore EH// AD$.
(2)由(1)得$AB// GD$,
$\therefore ∠2=∠BAD,∠DGC=∠BAC$.
$\because ∠DGC=58°,∴∠BAC=58°$.
$\because EH// AD,\therefore ∠2=∠H$,
$\therefore ∠H=∠BAD$,
$\therefore ∠BAC=∠BAD+∠4=∠H+∠4=58°$.
$\because ∠H=∠4+10°$,
$\therefore ∠4+10°+∠4=58°$.
解得$∠4=24°,∴∠H=34°$.

18.如图16，B，E分别是AC，DF上的一点，已知∠1=∠2，∠C=∠D.求证：∠A=∠F.

18. 证明: $\because ∠1=∠2,∠2=∠3$,
$\therefore ∠1=∠3$.
$\therefore BD// CE$.
$\therefore ∠C=∠DBA$.
$\because ∠C=∠D$,
$\therefore ∠D=∠DBA$.
$\therefore DF// AC$.
$\therefore ∠A=∠F$.