一、填空题
1. 已知$△ ABC ≌ △ A'B'C'$，$∠ A = ∠ A'$，$∠ B = ∠ B'$，$∠ C = 70°$，$AB = 15\ \mathrm{cm}$，则$∠ C' =$ $°$，$A'B' =$ $\mathrm{cm}.$

1. 70 15

2. 如图,$△ ABC ≌ △ EBD$. 若$∠ E=50°$,$∠ D=62°$,则$∠ ABC$的度数为.

2. 68°

3. 如图,$△ ABC ≌ △ DEF$,点$E,C$在线段$BF$上.若$BF=16,BC=12$,则$EC$的长为.

3. 8

4. 如图,在$△ ABC$中,$AD$是边$BC$上的高,点$E$在$AD$上. 若$△ ACD ≌ △ BED$,$BE=20$,$BC=28$,则$△ ACD$的周长为.

4. 48

二、解答题
5. 如图,$△ ABC ≌ △ DEB$,且点 D 在边 BC 上.
(1) 求证:$AC // BE$;
(2) 若$AC=4$,$CD=6$,求 BE 的长.

5. (1) $\because △ ABC ≌ △ DEB, \therefore ∠ C = ∠ DBE.$
$\therefore AC// BE$
(2) $\because △ ABC ≌ △ DEB, \therefore BC = EB, CA = BD = 4. \therefore BE = BD + CD = 10,$ 即 $BE$ 的长为 10

6. 如图,$△ ABC ≌ △ DEB$,点$E$在$AB$上,$DE$与$AC$相交于点$F$.
(1) 当$DE=8$,$BC=5$时,求$AE$的长;
(2) 若$∠ D=35°$,$∠ C=60°$,求$∠ DBC$,$∠ AFD$的度数.

6. (1) $\because △ ABC ≌ △ DEB, \therefore AB = DE, BC = EB.$
$\because DE=8,BC=5, \therefore AB=8,EB=5. \therefore AE=AB-EB=8-5=3$
(2) $\because △ ABC ≌ △ DEB, \therefore ∠ A = ∠ D, ∠ C = ∠ DBE. \because ∠ D=35°, ∠ C=60°, \therefore ∠ A=35°, ∠ DBE = 60°. \because ∠ A + ∠ ABC + ∠ C = 180°,$
$\therefore ∠ ABC = 180° - ∠ A - ∠ C = 85°. \therefore ∠ DBC = ∠ ABC - ∠ DBE = 85° - 60° = 25°. \because ∠ AEF$ 是 $△ DEB$ 的外角, $\therefore ∠ AEF = ∠ D + ∠ DBE = 35° + 60° = 95°.$
$\because ∠ AFD$ 是 $△ AEF$ 的外角, $\therefore ∠ AFD = ∠ A + ∠ AEF = 35° + 95° = 130°$