题目

在直角△ABC中，∠BAC=90°，BF平分∠ABC，∠AEF=∠AFE． （1）求证：AD⊥BC（请用一对互逆命题进行证明） （2）写出你所用到的这对互逆命题．     答案：（1）证明：在直角△ABC中， ∵∠BAC=90° ∴∠1+∠AFE=90° ∵BF平分∠ABC ∴∠1=∠2 ∵∠AEF=∠AFE 又∵∠3=∠AEF ∴∠3=∠AFE ∴∠2+∠3=90° ∴∠BDE=90° ∴AD⊥BC； （2）互逆命题：直角三角形的两锐角互余；有两个锐角互余的三角形是直角三角形．    （1）SUMMER JOB        Do you like to talk with people? Do you like to write stories? If you want to work for our magazine as a reporter, please call Karen at 558366．        （2）WANTED        Are you hard-working? Do you like to meet people? If your answer is “Yes”, then we have a job for you as a waiter．Call AI Hotel at 556779．        （3）HELP WANTED        Do you like babies? Can you look after a baby for two days? If you are sure to take good care of it, call us at 766588．$ 80 or more．Today! Hurry!        （4）CLEANER WANTED        Can you make a large house clean and tidy? If you hope to get the job paid at $ 20 once, call us this evening 18:00——20:00．        Tel: 633800 1．Where can you probably find the ads above?        A．A newspaper．    B．A report．           C．A guide book．    D．A science book． 2．If you like children and have two days free, you can call    for a job．        A．556779               B．558366                C．766588               D．633800 3．If you are a college student of English who enjoys writing, during your summer holidays you will be more interested in the job in    ．        A．ad．1             B．ad．2            C．ad．3             D．ad．4