在等腰三角形ABC中AB=AC=5,BC=6,点E是BC边上的一点,ED垂直于AB交AB边于点D,EF垂直于BC
等腰三角形ABC中,AB=AC=5,BC=6,E是BC上一点,ED⊥AB交AB于D,EF⊥BC交AC于F(1)三角形EDF能是等腰三角形吗?能,求CE(2)三角形EDF能...
等腰三角形ABC中,AB=AC=5,BC=6,E是BC上一点,ED⊥AB交AB于D,EF⊥BC交AC于F(1)三角形EDF能是等腰三角形吗?能,求CE(
2)三角形EDF能是直角三角形吗?能,求CE 展开
2)三角形EDF能是直角三角形吗?能,求CE 展开
2个回答
展开全部
做AG垂直BC,AGB为3-4-5直角三角形,AG= 4,
FEC-BDE-AGB为相似直角三角形
设BD= x, 则BE=5x/3, DE = 4x/3, CE = 6 - 5x/3, FE = 4/3 CE = 4/3 (6-5x/3) = 8 - 20x/9
FE = DE, 4x/3 = 8 - 20x/9, x = 9/4
CE = 6 - 5/3 * 9/4 = 6 - 15/4 = 9/4
<FED = <ABC,如果<DFE = 90度,则需满足FE/DE = 3/5, 即 3DE= 5FE
4x = 40 - 100x/9, x = 45/17
CE = 6 - 5/3 * 45/17 = 6 - 150/34 = 27/17
FEC-BDE-AGB为相似直角三角形
设BD= x, 则BE=5x/3, DE = 4x/3, CE = 6 - 5x/3, FE = 4/3 CE = 4/3 (6-5x/3) = 8 - 20x/9
FE = DE, 4x/3 = 8 - 20x/9, x = 9/4
CE = 6 - 5/3 * 9/4 = 6 - 15/4 = 9/4
<FED = <ABC,如果<DFE = 90度,则需满足FE/DE = 3/5, 即 3DE= 5FE
4x = 40 - 100x/9, x = 45/17
CE = 6 - 5/3 * 45/17 = 6 - 150/34 = 27/17
推荐律师服务:
若未解决您的问题,请您详细描述您的问题,通过百度律临进行免费专业咨询