三角形性質 數學工課3頁 急要答案

1.
(i)
等邊三角形

(ii)
等腰三角形


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2.
(i)
C + 3 = 8 (等腰Δ兩等邊)
c = 5

(ii)
2d = 5 (等腰Δ兩等邊)
d = 2.5


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3.
b + 88° + 53° = 180° (Δ內角和)
b = 39°


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4.
d = 30° + 45° (Δ外角)
d = 75°


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5.
y + (y + 30°) + (2y - 50°) = 180° (Δ內角和)
4y = 200°
y = 50°


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6.
∠ACB = 87° (等腰Δ兩底角)

∠ACB = b + 41° (Δ外角)
87° = b + 41°
b = 46°


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7.
2x + 60° = x + (3x + 10°)
2x + 60° = 4x + 10°
2x = 50°
x = 25°


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8.
∠MOP = ∠MPO (等腰Δ兩底角)
但 ∠MOP + ∠MPO + 56° = 180° (Δ內角和)
所以 2∠MOP = 124°
∠MOP = 62°

∠NOM = a (等腰Δ兩底角)

MN//OP (已知)
a + ∠NOP = 180° (同旁內角 MN//OP)
a + (∠NOM + ∠MOP) = 180°
a + (a + 62°) = 180°
2a = 118°
a = 59°

b + ∠NOM = 180° (直線同側鄰角和)
b + 59° = 180°
b = 121°