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ABC is a right triangle in which ∠B = 90°. D is a point on BC such that DC=AB. DE and BF are perpendicular to AC. If BF = 4cm, then CE+BF =________

ABC is a right triangle in which B 90 D is a point on BC such that DCAB DE and BF are perpendicular to AC If BF 4cm then CEBF class=

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linhle280807

Answer:

Step-by-step explanation

taco: góc FBC + góc FBA = 90° mà góc FBA + góc FAB = 90

⇒góc FAC = góc FBC mà góc FBC = góc EDC ⇒ góc FAC = góc EDF

xét Δ ABF và Δ DCE có

góc FAC = góc EDF

góc F = góc E = 90°

⇒ tam giác ABF đồng dạng với tam giác DCE

⇒ AB/DC = BF/EC ⇒ AB.EC = DC.BF mà AB = DC ⇒ EC=BF=4

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