英文四邊形數學題2(15分)

2009-02-05 4:34 am

請依下圖列出所有步驟及理據(如:int. angles, PQ//SR)等
題目可能包含mid-point theorem或intercept theorem

圖:http://i246.photobucket.com/albums/gg119/FFS12/ABC5-1.jpg

回答 (1)

用戶246859

2009-02-05 7:05 am

✔ 最佳答案

(a)
Consider triangle PAB & triangle PQR
Since both A & B are mid points of PQ & PR respectively,
PA:PQ = PB:PR, therefore triangle PAB & triangle PQR are similar triangles, and AB // QR.
Since ABS is straight line, so BS // QR
Similarly, for triangle PBC and triangle PRS,
B & C are mid points of PR & PS respectively,
PB:PR = PC:PS, therefore triangle PBC and triangle PRS are similar triangles and QB // RS.
Since QBC is straight line, QC // RS
Since BS // QR & QB // RS, so BQRS is a parallelogram,
(b)
From triangle PBC & triangle PRS, they are similar triangles with PB:PR=PC:PS = 1:2, so
BC:RS = 1:2
Since BQRS is a parallelogram, so QB = RS
Therefore, BC:QB=1:2, or QB=2BC

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