1.圖中,ABCD是平行四邊形,AE和CF都與BD垂直,求證AE=CF
*所有圖片可能會LOAD得比較慢
圖→http://space.netvigator.com/resources/0025556702/Q1.bmp
2.圖中,ABCD和AEFG都是正方形.求証角ABE=角ADG
圖→http://space.netvigator.com/resources/0025556702/Q2.bmp
3.圖中,D,E和F分別為直角等腰三角形ABC的三條邊AC,AB和BC的中點.
A)求證DEF是直角等腰三角形.
B)若三角形ABC的面積為32 CM^2,求三角形DEF的面積
圖→http://space.netvigator.com/resources/0025556702/Q3.bmp
F.3 Maths........20 marks
2007-03-13 7:20 am
回答 (2)
2007-03-14 7:06 am
✔ 最佳答案
1.∠AED =∠CFB=90°(property of square)
∠ADE =∠CBF (alt.∠s, AD // CB )
AD = BC (opp.sides equal))
△ADE≌△CBF( ASS )
AE = CF(corr. ∠s, ≌△s)
2.
∠GAD =∠EAB
AE = AG(property of square)
AD = AB(property of square)
△ABE≌△ADG(SAS)
∠ABE =∠ADG(corr. sides, ≌△s)
3.
A.)
AB/DF=2 (mid-pt. theorem)
CB/DE=2 (mid-pt. theorem)
AC/EF=2(mid-pt. theorem)
ABC ~ FDE (SSS)
△DEF also a isosceles triangle
B.)
AB = 2DF (mid-pt. theorem)
CB = 2DE (mid-pt. theorem)
area of DEF
= 1/2 x DF x DE
= 1/2 x (1/2xAB)x(1/2xCB)
= 1/4 x1/2xABxCB
= 1/4 x 32
= 8cm^2
2007-03-13 10:15 am
呢度我打唔到符號, 所以用中文加英文, 請見諒...
1.
< AED = < CFB ( = 90度 )
< ADE = < CBF ( AD // CB )
AD = BC ( ABCD 係 平行四邊形 )
==> ADE 全等 CBF ( ASS )
==> AE = CF
2.
< GAD = < EAB
AE = AG ( AEFG 係正方形)
AD = AB ( ABCD 係正方形 )
==> ABE 全等 ADG
==> < ABE = < ADG
3.
A.)
AB // DF ( mid point )
CB // DE ( mid point )
AC // EF ( mid point )
==> ABC ~ FDE (SSS)
==> DEF also 直角等腰
B.)
AB = 2DF ( mid point )
CB = 2DE ( mid point )
==>
area of DEF
= 1/2 * DF * DE
= 1/4 * 1/2 * AB * CB
= 1/4 area of ABC
= 1/4 * 32
= 8cm^2
1.
< AED = < CFB ( = 90度 )
< ADE = < CBF ( AD // CB )
AD = BC ( ABCD 係 平行四邊形 )
==> ADE 全等 CBF ( ASS )
==> AE = CF
2.
< GAD = < EAB
AE = AG ( AEFG 係正方形)
AD = AB ( ABCD 係正方形 )
==> ABE 全等 ADG
==> < ABE = < ADG
3.
A.)
AB // DF ( mid point )
CB // DE ( mid point )
AC // EF ( mid point )
==> ABC ~ FDE (SSS)
==> DEF also 直角等腰
B.)
AB = 2DF ( mid point )
CB = 2DE ( mid point )
==>
area of DEF
= 1/2 * DF * DE
= 1/4 * 1/2 * AB * CB
= 1/4 area of ABC
= 1/4 * 32
= 8cm^2
收錄日期: 2021-04-12 23:25:13
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070312000051KK05265