中二升中三數學題目第4問(20點)

Consider triangle XYO
XY^2 = XO^2 + YO^2 (Pythagorean Theorem)
(5 cm)^2 = XO^2 + (3 cm)^2
XO = square root of (25 – 9)
XO = square root of (16 cm^2)
XO = 4 cm

Consider triangle MNO
MN = 10 cm, NO = 6 cm, MO = 8 cm

Consider triangle XYO
XY = 5 cm, YO = 3 cm, XO = 4 cm
MN/XY = 10 cm/5 cm= 2
NO/YO = 6 cm/3 cm = 2
MO/XO = 8 cm/4 cm = 2

Two triangles are similar if the three pairs of corresponding sides are proportional.
triangle XYO ~ triangle MNO

XOY perimeter(周界) = XY + XO + YO = 5 cm +4 cm + 3 cm = 12 cm
XOY周界 = 12 cm

(a) 利用畢氏定理可以知道 X-O邊等於4
而 N-O邊長等於兩倍Y-O邊長
M-O邊長等於兩倍X-O邊長
M-N邊長等於兩倍X-Y邊長
再利用相似三角形SSS性質(S是邊長 A是角度)
證明 三角形MNO~XYO

(b) 則三角形XOY的周長
三個邊都知道了
那就是3+4+5=12