在Rt三角形ABC中,角ACB=90度,CD垂直AB于D,E为AC的中点,ED的延长线交CB的延长线于P.
求证:PD的平方=PB×PC
人气:303 ℃ 时间:2019-10-23 08:56:15
解答
证明:ED是直角△ADC的斜边AC上的中线,∴ED=EC,∴∠ECD=∠EDC
∴∠ECD+90°=∠EDC+90°,∴∠PCD=∠PDB
又∵∠P=∠P,∴△PCD∽△PDB
∴PC:PD=PD:PB,∴PD的平方=PB×PC
推荐
猜你喜欢
- heard和listen to的意思是一样的吗?
- 世界是四大吝啬鬼分别是谁?
- The house ______ they live in was built hundreds of years ago.怎么填
- They make you feel like less of a person so you will buy their stuff.分析一下这句话
- 一个数除以8余7,除以12余11,这个数最小是多少,在1000以内,这样的数有几个?
- Where's my mother?She isn't here.She has gone to the butcher's.怎么翻译?
- At the moment ,my cousin Jim ____ (play) computer games.怎么填
- 找规律填数1,2,3,5,8,,,64,81.请问?处填什么数字