英文四邊形數學題(20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/ABC4.jpg

回答 (1)

用戶246859

2009-02-05 7:15 am

✔ 最佳答案

(a)
Consider triangles PGF & PRS,
PF:PS=PG:PR=1:2
Therefore, triangle PGF & PRS are similar triangles, so
FG:SR = 1:2
Since SR = 10cm, so FG = 5cm
(b)
Since FH is 7cm, so GH is 2cm
Consider triangle RGH & triangle RPQ,
RG:RP=RH:RQ=1:2
Therefore triangles RGH & RPQ are similar triangles, so
GH:PQ=1:2
Since GH is 2cm, so PQ is 4cm
(c)
Since triangles PGF & PRS are similar triangles and PF:PS=PG:PR= 1:2, so FG // SR
Similarly, triangles RGH is similar to triangle RPQ are GH // PQ,
since FGH is straight line, so
PQ//FH//SR
Therefore angle QPS + angle PSR = 180o
or angle QPS = 180o - 75o
= 105o

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