第15页 - 通城学典课时作业本八年级数学苏科版江苏专版

$65^{\circ}$

$AB// DC$

$ (1)$证明：∵$AD = BE$

∴$AD + BD = BE + BD，$即$AB = DE$

$ $在$\triangle ABC$和$\triangle DEF $中

$ \begin {cases}AB = DE \\AC = DF \\BC = EF\end {cases}$

∴$\triangle ABC≌\triangle DEF(\mathrm {SSS})$

$ (2)$解：∵$\triangle ABC≌\triangle DEF，$$∠A = 55°$

∴$∠A = ∠F DE = 55°$

∵$\triangle DEF $的内角和为$180°，$$∠E = 45°$

∴$∠F = 180° - (∠F DE + ∠E)=180° - (55° + 45°) = 80°$

$ (1)$证明：连接$AB$

$ $在$\triangle ABC$和$\triangle ABD$中

$ \begin {cases}AC = AD \\AB = AB \\BC = BD\end {cases}$

∴$\triangle ABC≌\triangle ABD(\mathrm {SSS})$

∴$∠C = ∠D$

$ (2)$解：∵$\triangle ABC≌\triangle ABD$

∴$∠CAB = ∠DAB = \frac 12∠CAD，$$∠ABC = ∠ABD$

∵$∠CBD = 120°$

∴$∠ABC = \frac 12(360° - ∠CBD)=120°$

∵在$\triangle ABC$中，$∠C = 28°$

∴$∠CAB = 32°$

∴$∠CAD = 2∠CAB = 64°$

C