Angle Bisector and the Longest Side
2019-08-08 06:32
This GeoGebra mathematics example demonstrates the geometric relationship between an angle bisector and the opposite side in a triangle. By constructing polygons, segments, and angles, it visually illustrates the Angle Bisector Theorem and its application to the ratio of side lengths, aiding learners in understanding the geometric properties of an angle bisector dividing the opposite side.
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求试：BF=BD""/>
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在AC上取B'，使AB'=AB，
连接DB’∵∠1=∠2，AD=AD，AB=AB’，
∴ΔADB≌ΔADB'；
∠ADB=∠ADB'∴BD=AC-AB'=B'C，∴∠B'DC=∠C
结论1：∠BFD=∠1+∠3；（ΔABF的外角）

∠ADB+∠ADB'+∠C=180°，∴∠ADB=（180°-∠C）/2
又∵∠C=180-2∠1-2∠3 （ΔABC内角和)∴∠ADB=（180°-∠C）/2=(180°-180+2∠1+2∠3 ）/2
结论2∴∠ADB=∠1+∠3∴∠ADB=∠BFD
∴BF=BD（等腰三角形性质）证毕 ""/>
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