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20. (本小题 8 分)完成下面的证明:
如图,$AD⊥ BC$,$FG⊥ BC$,垂足分别为$D$,$G$,且$∠ GFC = ∠ ADE$.求证:$DE// AC$.
证明:$\because AD⊥ BC$,$FG⊥ BC$(已知)
$\therefore∠ ADC =$,$∠ FGC =$(垂直的定义),
$\therefore∠ ADC = ∠ FGC$.
$\therefore AD//$(同位角相等,两直线平行).
$\therefore∠ DAC = ∠ GFC$().
又$\because∠ GFC = ∠ ADE$(已知),
$\therefore∠ DAC = ∠ ADE$.
$\therefore DE// AC$().
如图,$AD⊥ BC$,$FG⊥ BC$,垂足分别为$D$,$G$,且$∠ GFC = ∠ ADE$.求证:$DE// AC$.
证明:$\because AD⊥ BC$,$FG⊥ BC$(已知)
$\therefore∠ ADC =$,$∠ FGC =$(垂直的定义),
$\therefore∠ ADC = ∠ FGC$.
$\therefore AD//$(同位角相等,两直线平行).
$\therefore∠ DAC = ∠ GFC$().
又$\because∠ GFC = ∠ ADE$(已知),
$\therefore∠ DAC = ∠ ADE$.
$\therefore DE// AC$().
答案
$90^{\circ}$；$90^{\circ}$；$FG$；两直线平行，同位角相等；内错角相等，两直线平行
解析
$\because AD⊥ BC$,$FG⊥ BC$(已知)
$\therefore∠ ADC = 90^{\circ}$,$∠ FGC = 90^{\circ}$(垂直的定义),
$\therefore∠ ADC = ∠ FGC$.
$\therefore AD// FG$(同位角相等,两直线平行).
$\therefore∠ DAC = ∠ GFC$(两直线平行，同位角相等).
又$\because∠ GFC = ∠ ADE$(已知),
$\therefore∠ DAC = ∠ ADE$.
$\therefore DE// AC$(内错角相等，两直线平行).
$\therefore∠ ADC = 90^{\circ}$,$∠ FGC = 90^{\circ}$(垂直的定义),
$\therefore∠ ADC = ∠ FGC$.
$\therefore AD// FG$(同位角相等,两直线平行).
$\therefore∠ DAC = ∠ GFC$(两直线平行，同位角相等).
又$\because∠ GFC = ∠ ADE$(已知),
$\therefore∠ DAC = ∠ ADE$.
$\therefore DE// AC$(内错角相等，两直线平行).
