中五三角形~

1.
4x + 45o = 2x + 5x (ext. of D)
3x = 45o
x = 15o


2.
FDE + FED = CFE (D外角)
FDE + 32o = 100o
FDE = 68o

BC // DC
BDF + FDE = ABC (// 同位角)
BDF + 68o = 116o
BDF = 48o


3.
經過 C，作一直線 HCK // AB // DE。
A、H、D 在同一邊，而B、K、E 在同一邊。

ACH = BAC (// 內錯角)
ACH = 3x

DCH = CDE
DCH = 7x

ACD = ACH + DCH
4x + 60o = 3x + 7x
6x = 60o
x = 10o


4.
設 ABH = x
HBC = ABH (己知)
HBC = x

ABC = ABH + HBC (BHK 是 ABC 分角線)
ABC = 2x

AB = AC (已知)
ACB = ABC (等腰D底角)
ACB = 2x

ABC + ACB + BAC = 180o (D內角和)
2x + 2x + 40o = 180o
4x = 140o
x = 35o

CHK = HBC + ACB (D外角)
CHK = x + 2x
CHK = (35o) + 2(35o)
CHK = 105o


5.
ACD + 130o = 180o (同側鄰角和)
ACD = 50o

CAD + 148o = 180o (同側鄰角和)
CAD = 32o

BEC + 154o = 180o (同側鄰角和)
BEC = 26o

ADE = ACD + CAD (D外角)
ADE = 50o + 32o
ADE = 82o

x = ADE + BEC (D內角)
x = 82o + 26o
x = 108o
=

1.
2X + 5X = 4X + 45 (Δ外角)
3X = 45
X = 15

2.
∠EDF + 32 = 100 (Δ外角)
∠EDF = 68

∠BDE = 116 (同位角,BC//DE)

∠BDF + ∠EDF = ∠BDE
∠BDF + 68 = 116
∠BDF = 48

3.
∠ABC = 7X (錯角,AB//DE)

∠ABC + ∠BAC = ∠ACD (Δ外角)
7X + 3X = 4X + 60
6X = 60
X = 10

4.
∠ABC = ∠ACB (等腰Δ底角)
∠ABH + ∠CBH = ∠ACB
∴2∠CBH = ∠ACB (因為ＢＨＫ是∠ＡＢＣ的角平分線∴∠ABH = ∠CBH)
∠ABC + ∠ACB +40 = 180
2∠ACB + 40 = 180
∠ACB = 70
∴∠CBH = 35

∠CHK = ∠ACB + ∠CBH
∠CHK = 70 + 35
∠CHK = 105

5.
∠CAD + 148 = 180 (直線上的鄰角)
∠CAD = 32

∠ACD + 130 = 180 (直線上的鄰角)
∠ACD = 50

∠BEC + 154 = 180 (直線上的鄰角)
∠BEC = 26

∠ADE = ∠CAD + ∠ACD
∠ADE = 32 + 50
∠ADE = 82

AFE = ∠ADE + ∠BEC
X = 82 + 26
X = 108

2009-02-04 00:25:46 補充：
∠ADE = ∠CAD + ∠ACD(Δ外角)

∠ADE = 32 + 50

∠ADE = 82



AFE = ∠ADE + ∠BEC(Δ外角)

X = 82 + 26

X = 108