PROVE RHOMBUS and RECTANGLE

[匿名]

2008-04-13 10:04 pm

I am a S.3 student only, don't use higher form Maths to teach me.

In Deductive Geometry
(NOT Coordinate Geometry NOR Analytical Geometry),

如何PROVE一個四邊形係RHOMBUS呢?
如何PROVE一個四邊形係RECTANGLE呢?

I don't want "property of rhombus" nor "property of rectangle".
I don't want to prove by "distance formula" nor "slope formula".
I want to prove by Deductive geometry ONLY
(similar to "opp. sides equal" "opp. angles equal" "diags. bisect each other" "two sides equal and //" in proving //gram)
(similar to "http://hk.knowledge.yahoo.com/question/?qid=7007040604231").

Chinese or English are both ok.

盡量多D方法, 吾該:)

更新1:

For rectangle, I think to prove 3 right angles is ok!

回答 (1)

Chui Ling

2008-04-13 11:48 pm

✔ 最佳答案

因為rhombus and rectangle are both a type of parallelgram
so you should first prove they are parallelgram by opp. sides equal, opp. angles equal, diags. bisect each other, or two sides equal and //

Then, for rhombus,
the definition of rhombus is parallelgram which have four equal sides
so we need to prove the four sides are equal

for rectangle,
the definiton of rectangle is parallelgram which have four right angles
so we need to prove the four angles of parallelgram are right angle

參考: my math knowledge

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