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As shown in the figure, D in △ ABC is any point on edge BC, de and DF are bisectors of △ ADB and △ ADC respectively, connecting EF. Try to judge the shape of △ def and explain the reason
∵ de and DF are the bisectors of △ ADB and △ ADC, respectively, ∵ ade = ∵ BDE, ∵ ADF = ∵ CDF, ∵ EDF = ∵ ade + ∵ ADF = 12 × 180 ° = 90 °, ∵ DEF is a right triangle
In the triangle ABC, ab = AC, D is a point on AB, extend AC to point E, make CE = BD, connect de and intersect BC at point F
In fact, it is the last question on page 43 of volume B of junior high school mathematics in Grade 8 of Qingpu experimental middle school
Certification:
Do DG ‖ AC, intersect BC at point G
Then ∠ DGB = ∠ ACB
∵AB=AC
∴∠ABC=∠ACB
∴∠ABC=∠DGB
∴BD=DG=CE
∵∠FDG=∠E,∠DFG=∠CFE
∴△FDG≌△FEC
∴DF=EF
As shown in the figure, D is the point on the edge BC of △ ABC, and CD = AB, ∠ ADB = ∠ bad, AE is the middle line of △ abd
As shown in the figure, D is a point on the BC side of △ ABC, and CD = AB, ∠ BDA = ∠ bad, AE is the middle line of △ abd
It is proved that: extend AE to F, make ef = AE, connect DF, ∵ AE is the middle line of △ abd ∵ be = ed, in △ Abe and △ FDE, ∵ be = de ∠ AEB = defae = EF, ≌ Abe ≌ FDE (SAS), ∵ AB = DF, ? Bae = EFD, ? ADB is the outer angle of △ ADC, ? DAC + ≌ ACD = ≌ ADB = bad, ≌
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