中三-數學[20點]

1a.
x=55
y=4
1b.
x=90
y=3/2
2a.
x=4.5
2b.
x=3
3a.
x=2
y=2
3b.
x=2.5
y=2.5
z=2.5
4a.
YES
4b.
YES

1(a).
because △AMN〜△ABC
so x=∠AMN=55°
and 2:y = 1:2
so y = 4


1(b). same as (a) △BMN〜△BAC
∴x = 90°, y=3/2

2(a). AD//BE//CF
∴ AB:BC = DE:EF
∴ x =4.5

2(b). same as 2(a), x = AC = 3

3(a). x:y = AM:MB = 3:3 so x=y
And also x+y=4
∴x=y=2

3(b). because ∠B=∠C=60°
∴ △ABC & △MBN 為等邊三角形
∴ x=y=z=2.5

4(a). yes ( MN:x = AM:AB = 1:2 )

4(b). yes same as 4(a)

1(a)x=55
y=4
1(b)x=90
y=3/2
2(a)x=4.5
2(b)x=3
3(a)x=2
y=2
3(b)x=2.5
y=2.5
z=2.5
4(a)YES
4(b)NO