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As shown in the figure, in △ ABC, point E is on AB, point D is on BC, BD = be, ∠ bad = ∠ BCE, ad and CE intersect at point F. try to judge the shape of △ AFC and explain the reason
The reasons are as follows: in △ bad and △ BCE, ∩ B = ∩ B (common angle), ∩ bad = ≌ BCE, BD = be, ≌ bad ≌ BCE (AAS), ∩ Ba = BC, ≌ bad = ≌ BCE, ∩ BAC = ∩ BCA, ∩ BAC - ≌ bad = ∩ BCA - ≌ BCE, namely ∩ fac = ≌ FCA, ≌ AF = CF, ∩ AFC is an isosceles triangle
RELATED INFORMATIONS
- 1. It is known that, as shown in the figure, D is a point inside △ ABC connecting BD and ad, with BC as the edge, outside △ ABC, make ﹥ CBE = ﹥ abd, ﹥ BCE = ﹥ bad, be and CE cross to e, connecting de. (1) verification: bcab = bebd; (2) verification: ﹥ DBE ﹥ ABC
- 2. As shown in the figure, D is a point inside the triangle ABC, connecting BD and ad, taking BC as the edge, making an angle outside the triangle ABC, CBE = angle abd, BCE = angle bad, be, CE intersecting at point E, connecting de. prove that the triangle DBE is similar to the triangle ABC
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- 5. As shown in the figure, ad and be are the heights of BC and AC respectively in ABC
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