Easy Maths question!

Given AB//DC and AD//BC
Hence, by the rule of int. ∠s, // lines
∠A + ∠D = 180 deg (int. ∠s, AB//DC) -----(1)
∠D + ∠C = 180 deg (int. ∠s, AD//BC)
∠D = 180 deg - ∠C -----(2)
Put (2) into (1),
∠A + 180 deg - ∠C = 180 deg
∠A = ∠C
ABCD is a //gram. (opp. ∠s equal)

However, in here, the meaning of //gram is quite vague as it doesn't give the figure for the ∠s and the sides.

if ∠A = ∠B = ∠C = ∠D = 90 deg and AB = BC = CD = AD,
it is a square.
If ∠A = ∠B = ∠C = ∠D = 90 deg and AB = CD, AD = BC,
it is a rectangle.
If ∠A = ∠C , ∠B = ∠D and AB = BC = CD = AD,
it is a rhombus.
If it doesn't satisfy the above conditions, it certainly can be a //gram.

定義 can't prove ...

To 001,我曾經思考此問題,我的方法與你差不多.

假設你的証明成立,為何(對邊平行)不能作為証明平行四邊形的原因呢??

2010-12-10 16:38:39 補充：
但你的証明方法有很多步驟沒有寫出來.(在此題中不是大問題)

2010-12-10 17:19:42 補充：
To 003,有此証明原因咩?

2010-12-10 17:58:49 補充：
明白了..................

Line AB is parallel to Line DC
Line AD is parallel to Line BC

Angle ADC =Angle ABC
Angle BAD = Angle BCD

Length AB = Length DC
Length AD = Length BC