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7. 如图，已知△ABC≌△DEB，点E在AB上，AC与BD交于点F，AB＝12.5，BC＝5，∠C＝65°，∠D＝20°.求：(1) AE的长度；(2) ∠AED的度数.
答案
(1) 7.5
(2) $85°$
(2) $85°$
8. 如图,点B,C,D在同一条直线上,∠B=∠D=90°,△ABC≌△CDE,AB=7,BC=24,CE=25.求:
(1)△ABC的周长；
(2)△ACE的面积.
(1)△ABC的周长；
(2)△ACE的面积.
答案
(1) $\because △ ABC ≌ △ CDE, CE=25, \therefore AC=CE=25. \because AB=7, BC=24, \therefore △ ABC的周长为AB+BC+AC=7+24+25=56.$
(2) $\because ∠ B=90°, \therefore ∠ ACB + ∠ BAC =90°. \because △ ABC ≌ △ CDE, \therefore ∠ ECD = ∠ BAC. \therefore ∠ ACB + ∠ ECD =90°. \because 点B,C,D在同一条直线上, \therefore ∠ ACB + ∠ ECD + ∠ ACE =180°. \therefore ∠ ACE=90°. \because AC=CE=25, \therefore △ ACE的面积为\frac{1}{2} × 25 × 25 = \frac{625}{2}.$
(2) $\because ∠ B=90°, \therefore ∠ ACB + ∠ BAC =90°. \because △ ABC ≌ △ CDE, \therefore ∠ ECD = ∠ BAC. \therefore ∠ ACB + ∠ ECD =90°. \because 点B,C,D在同一条直线上, \therefore ∠ ACB + ∠ ECD + ∠ ACE =180°. \therefore ∠ ACE=90°. \because AC=CE=25, \therefore △ ACE的面积为\frac{1}{2} × 25 × 25 = \frac{625}{2}.$
