中三數學幾題.急.20分thz@@@@@@@@@@@@@@@

1.
∠SRQ = ∠P擔 = 180ﾟ (同旁內角, PQ 平衡 SR)
∠SRQ = 180ﾟ - 76ﾟ = 104ﾟ
∠SRP = ∠PRS (菱形性質)
∠SRP = 104ﾟ /2 = 52ﾟ
∠SRT = ∠TRP (已知)
∠SRT = 52ﾟ /2 = 26ﾟ
∠S = ∠Q = 76ﾟ (菱形性質)
在 △STR中, ∠PTR = ∠S + ∠SRT (△外角)
= 76ﾟ + 26ﾟ = 102ﾟ
2.
∠BAD = 180ﾟ - 132ﾟ = 48ﾟ (同旁內角, AB 平衡 DC)
∴ ∠BAK = ∠KAD (菱形性質)
∠BAK = 48ﾟ /2 = 24ﾟ
AB = AK (已知)
∠ABK = ∠AKB (等腰△底角)
∠BAK + ∠ABK + ∠AKB = 180ﾟ (△內角和)
∠AKB = [180ﾟ - 24ﾟ]/2 = 78ﾟ
∠EKC = ∠AKB = 78ﾟ (對頂角)
∠ACE = ∠BAK = 24ﾟ (內錯角, AB 平衡 DC)
∠ACE + ∠EKC + ∠BEC = 180ﾟ (△內角和)
∠BEC = 180ﾟ - 24ﾟ - 78ﾟ = 78ﾟ

3.
∠EBC + ∠BCF = 180ﾟ (同旁內角, BE 平衡 CF)
∠EBC = 180ﾟ - 110ﾟ = 70ﾟ
∠ABC = 90ﾟ (正方形性質)
∠ABE = ∠ABC + ∠EBC = 90ﾟ + 70ﾟ = 160ﾟ
AB = BC (正方形性質)
BC =BE (菱形性質)
∴ AB = BE
∠BAE = ∠BEA (等腰△底角)
∠BAE + ∠BEA + ∠ABE = 180ﾟ (△內角和)
∠BAE = [180ﾟ - 160ﾟ]/2 = 10ﾟ

4.
∠PQR = 45ﾟ (正方形性質) 或
(正方形對角線與每一條邊夾角成 45ﾟ )

自己做

1.
∠SRQ = ∠P擔 = 180ﾟ (同旁內角, PQ 平衡 SR)


∠SRQ = 180ﾟ - 76ﾟ = 104ﾟ


∠SRP = ∠PRS (菱形性質)


∠SRP = 104ﾟ /2 = 52ﾟ


∠SRT = ∠TRP (已知)


∠SRT = 52ﾟ /2 = 26ﾟ


∠S = ∠Q = 76ﾟ (菱形性質)


在 △STR中, ∠PTR = ∠S + ∠SRT (△外角)
= 76ﾟ + 26ﾟ = 102ﾟ


2.


∠BAD = 180ﾟ - 132ﾟ = 48ﾟ (同旁內角, AB 平衡 DC)


∴ ∠BAK = ∠KAD (菱形性質)


∠BAK = 48ﾟ /2 = 24ﾟ


AB = AK (已知)


∠ABK = ∠AKB (等腰△底角)


∠BAK + ∠ABK + ∠AKB = 180ﾟ (△內角和)


∠AKB = [180ﾟ - 24ﾟ]/2 = 78ﾟ


∠EKC = ∠AKB = 78ﾟ (對頂角)


∠ACE = ∠BAK = 24ﾟ (內錯角, AB 平衡 DC)


∠ACE + ∠EKC + ∠BEC = 180ﾟ (△內角和)


∠BEC = 180ﾟ - 24ﾟ - 78ﾟ = 78ﾟ





3.


∠EBC + ∠BCF = 180ﾟ (同旁內角, BE 平衡 CF)


∠EBC = 180ﾟ - 110ﾟ = 70ﾟ


∠ABC = 90ﾟ (正方形性質)


∠ABE = ∠ABC + ∠EBC = 90ﾟ + 70ﾟ = 160ﾟ


AB = BC (正方形性質)


BC =BE (菱形性質)


∴ AB = BE


∠BAE = ∠BEA (等腰△底角)


∠BAE + ∠BEA + ∠ABE = 180ﾟ (△內角和)


∠BAE = [180ﾟ - 160ﾟ]/2 = 10ﾟ





4.


∠PQR = 45ﾟ (正方形性質) 或


(正方形對角線與每一條邊夾角成 45ﾟ )

5,6,7,8,9,10 I do not know. \>---</