问一道数学题,写解题过程已知等腰三角形abc中,∠bac=90°,d是ac中点ae垂直bd交于e,交bc于f,连接df,求证:∠adb=∠cdf

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问一道数学题,写解题过程已知等腰三角形abc中,∠bac=90°,d是ac中点ae垂直bd交于e,交bc于f,连接df,求证:∠adb=∠cdf
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问一道数学题,写解题过程已知等腰三角形abc中,∠bac=90°,d是ac中点ae垂直bd交于e,交bc于f,连接df,求证:∠adb=∠cdf
问一道数学题,写解题过程
已知等腰三角形abc中,∠bac=90°,d是ac中点ae垂直bd交于e,交bc于f,连接df,求证:∠adb=∠cdf

问一道数学题,写解题过程已知等腰三角形abc中,∠bac=90°,d是ac中点ae垂直bd交于e,交bc于f,连接df,求证:∠adb=∠cdf
证明:  如图:过点C作AC的垂线交AF的延长线于K
             由题得:∠1=∠3 (同角的余角相等)
               BA=AC
                      ∠BAD=∠ACK=90°
                 ∴ △BAD≌△ACK (角、边、角)
            AD=CK    ∠4=∠6
                    ∵ AD=CD
                    ∴CK=CD
                 又∵ ∠DCF=∠KCF=45°
                          CF=CF
                   ∴△DCF ≌△KCF (边、角、边)(“≌ 表示“全等于”)
                ∴ ∠5=∠6
                          ∴∠4=∠5
                   即:∠ADB=∠CDF
                                     《证毕》!