英文數學題7,急急

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).

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..)