form 3 math (geometry)

1.∵AB/XY=3/4
AC/XZ=3/4
BC/YZ=3/4
i.e. AB/XY= AC/XZ= BC/YZ
∴ΔABC~ΔXYZ (3 sides prop.)

2. ∵AB/XY=10/5=2
AC/XZ=24/12=2
BC/YZ=26/13=2
i.e. AB/XY= AC/XZ= BC/YZ
∴ΔABC~ΔXYZ (3 sides prop.)
之後果兩個link都上唔到。

2009-03-24 21:52:14 補充：
2b)∵ΔABC~ΔXYZ (proved)
∴∠A=∠X=85∘(corr. ∠s, ~Δs)

2009-03-25 22:26:27 補充：
Classwork 10.7
1)∠ABC+∠ACB+∠BAC=180˚ (∠ sum of Δ)
60˚+∠ACB+50˚=180˚
∠ACB=70˚
∠PQR+∠PRQ+∠QPR=180˚ (∠ sum of Δ)
60˚+70˚+∠QPR=180˚
∠QPR=50˚
∠ABC=∠PQR=60˚
∠ACB=∠PRQ=70˚
∠BAC=∠QPR=50˚
∴ΔABC=ΔPQR (equiangular)

2009-03-25 22:26:38 補充：
2a) ∠ABC+∠ACB+∠BAC=180˚ (∠ sum of Δ)
90˚+∠ACB+30˚=180˚
∠ACB=60˚
∠PQR+∠PRQ+∠QPR=180˚ (∠ sum of Δ)
90˚+60˚+∠QPR=180˚
∠QPR=30˚
∠ABC=∠PQR=90˚
∠ACB=∠PRQ=60˚
∠BAC=∠QPR=30˚
∴ΔABC=ΔPQR (equiangular)

2b)BC/QR=AC/PR (corr. ∠s, ~Δs)
5/QR=10/15
5/QR=2/3
QR/5=3/2=1.5
QR=5×1.5
=7.5

2009-03-25 22:39:03 補充：
Classwork 10.8
1)AC=BC (given)
XZ=YZ (given)
∴AC/XZ=BC/YZ
∠ACB=∠XZY=90˚ (given)
∴ΔABC~ΔXYZ (ratio of 2 sides, inc. ∠)

2a)AX/AB=12/(12+6)=2/3
AY/AC=10/(10+5)=2/3
∴AX/AB=AY/AC
∠XAY=∠BAC (common ∠)
∴ΔAXY~ΔABC (ratio of 2 sides, inc. ∠)

2009-03-25 22:39:14 補充：
2b)XY/BC=AX/AB (corr. ∠s, ~Δs)
5/BC=2/3
BC/5=3/2=1.5
BC=5×1.5=7.5
樓上未做 Classwork 10.7 同 10.8。

2009-03-25 22:41:00 補充：
更正：
Classwork 10.7
2b)BC/QR=AC/PR (corr. sides,~Δs)
5/QR=10/15
5/QR=2/3
QR/5=3/2=1.5
QR=5×1.5=7.5

Classwork 10.8
2b)XY/BC=AX/AB (corr. sides,~Δs)
5/BC=2/3
BC/5=3/2=1.5
BC=5×1.5=7.5

10.6

a)
AB/XY =BC/YZ = AC/XZ =3/4

so ABC ~ XYZ ( 3 sides proportional )

b)AB/XY =BC/YZ = AC/XZ =1/2

so ABC ~ XYZ ( 3 sides proportional )

ii) A = 180 -B-C =180 -( Y-Z) =180 -( 70 +25) =85//



2009-03-24 21:39:49 補充：
http://hk.geocities.com/ew1368/CCF24032009_00005.jpg
http://hk.geocities.com/ew1368/CCF24032009_00006.jpg

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