標題:
英文數學題7,急急
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發問:
In the figure(http://hk.geocities.com/ken1ken1232003/TRI.bmp), AYC,ABX,CZX,BZYare straight lines, AB=AC and AX=AY. (a)Prove that △BCY=△CBX. (b)Prove that △BCZis an isosceles triangle.
最佳解答:
圖片參考：http://hk.geocities.com/ken1ken1232003/TRI.bmp In the figure AYC,ABX,CZX,BZYare straight lines, AB=AC and AX=AY. (a)Prove that △BCY=△CBX. (b)Prove that △BCZis an isosceles triangle. (a)可先證明△AXC=△AYB，再利用全等三角形性質求出△BCY=△CBX 在△AXC及△AYB中， AX = AY (已知) AB = AC (已知) ∠CAB = ∠CAB (公共角) ∴△AXC = △AYB (S.A.S.) ∵△AXC = △AYB (已證) ∴CX = BY (全等△的對應邊) CB = CB (公共邊) AX = AB + BX AY = AC + CY ∵AB = AC (已知) ∴BX = CY ∴△BCY = △CBX (S.S.S.) (b)Prove that △BCZis an isosceles triangle. ∵△BCY = △CBX (已證) ∴∠C = ∠B (全等△的對應角) ∴BZ = CZ (△中，等角對等邊) ∴△BCZ is an isosceles triangle (等腰三角形).
其他解答:
a) AX=AY (given) AC=AB (given) angleA=angleA so △AXC=△AYB (S.A.S) so CX=BY and angleX=angleY ( ) AX-AB=AY=AC so BX=BY so △BCY=△CBX (S.A.S) b) as △BCY=△CBX angleB=angleC ( ) so △BCZ is an isosceles triangle (因為有一排冇店過maths所以D ( ) 裏面的野唔記得左..)
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