题干

如图,四棱柱ABCD﹣A1B1C1D1中,侧面AA1D1D为矩形,AB⊥平面AA1D1D,CD⊥平面AA1D1D,E、F分别为A1B1、CC1的中点,且AA1=CD=2,AB=AD=1.

(1)求证:EF∥平面A1BC;

(2)求D1到平面A1BC1的距离.

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答案(点此获取答案解析)

证明:(1)取A1B的中点O,连接OE,OC,则OE平行且等于
1
2
BB1
∵F为CC1的中点,∴CF平行且等于1

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    Since 1989, Dave Thomas, who died at the age of 69, was one of the most recognizable faces on TV. He appeared in more than 800 commercials for the hamburger chain named for his daughter. “As long as it works”, he said in 1991, “I'll continue to do those commercials.”

    Even though he was successful, Thomas remained troubled by his childhood. “He still won't let anyone see his feet, which are out of shape because he never had proper fitting shoes,” Wendy said in 1993. Born to a single mother, he was adopted as a baby by Rex and Auleva Thomas of Kalamazoo in Michigan. After Auleva died when he was 5, Thomas spent years on the road as Rex traveled around seeking construction work. “He fed me,” Thomas said, “and if I got out of line, he'd beat me.”

    Moving out on his own at 15, Thomas worked, first as a waiter, in many restaurants. But he had something much better in mind. “I thought if I owned a restaurant,” he said, “I could eat for free.” A 1956 meeting with Harland Sanders led Thomas to a career as the manager of a Kentucky Chicken restaurant that made him a millionaire in 1968.

    In 1969, after breaking with Sanders, Thomas started the first Wendy's Old Fashioned Hamburgers, in Columbus, Ohio, which set itself apart by serving made-to-order burgers. With 6,000 restaurants worldwide, the chain now makes $ 6 billion a year in sales. Although troubled by his own experience with adoption, Thomas, married since 1954 to Lorraine, 66, and with four grown kids besides Wendy, felt it could offer a future for other children. He started the Dave Thomas Foundation for Adoption in 1992.

    In 1993, Thomas, who had left school at 15, graduated from Coconut Creek High School in Florida. He even took Lorraine to the graduation dance party. The kids voted him Most Likely to Succeed.

    “The Dave you saw on TV was the real Dave,” says friend Pat Williams. “He wasn't a great actor or a great speaker .He was just Joe Everybody.”