题目

如图，在△ABC中，AD平分∠BAC，AD⊥BD于点D，取BC的中点E，连结DE。 （1） 求证：DE∥AC； （2） 若AB=8，AC=12，求DE的长。 答案：证明：如图，延长BD交AC于点F. ∵AD平分∠BAC，∴∠BAD=∠FAD. ∵AD⊥BF，∴∠BDA=∠FDA. 又∵AD=AD. ∴△ABD≌△AFD（ASA），∴BD=FD. 又∵E为BC的中点，∴DE为△BCF的中位线. ∴DE∥FC，∴DE∥AC 解：由△ABD≌△AFD得AB=AF. ∴CF=AC-AF=AC-AB=12-8=4. ∵DE是△BCF的中位线，∴DE=12FC=2。5．Nelson Mandela，born（56）onJuly 18，1918，is the first black president of South Africa．He studied law（57）afterhe entered university．In 1944 he founded（58）theANC Youth League．Then in 1952 he set up a law office（59）to help（ help ） poor black people．Because of his（60）fighting（fight ） against the government and anti-black laws，he（61）was sentenced（ sentence ） to five years hard labor．Fighters from ANC began to blow up buildings in 1963（62）andhe was put in prison again for life imprison ment on Robben Island．Twenty-seven years later，he was freed at last by the white government．In 1993 he was made the（63）first（ one ） black president of South Africa．A lot of people in the world think Nelson Mandela is（64）really（ real ） a great person．（65）Whatdo you think of him？