In the figure,ABCD and AEFG are squares.Prove that∠ABE = ∠ADG.
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F.3(quadrilaterals)急!
2009-04-11 2:48 am
回答 (2)
2009-04-11 3:09 am
✔ 最佳答案
In triangle ABE and triangle ADG,AB = AD (properties of a square)
AE = AG (properties of a square)
∠DAB = ∠GAE = 1rt∠
∠DAB - ∠DAE = ∠GAE - ∠DAE
∠EAB = GAD
Triangle ABE and triangle ADG are congruent triangles (SAS)
∠ABE = ∠ADG (corresponding angles)
2009-04-11 3:01 am
Prove
AB=AD (given)
AE=AG (given)
∠GAE = ∠DAB=90
=>∠GAD+∠DAE = ∠DAE + ∠EAB
==>∠GAD = ∠EAB
So ADG~= ABE (SAS) and ∠ABE = ∠ADG
AB=AD (given)
AE=AG (given)
∠GAE = ∠DAB=90
=>∠GAD+∠DAE = ∠DAE + ∠EAB
==>∠GAD = ∠EAB
So ADG~= ABE (SAS) and ∠ABE = ∠ADG
參考: 現象背後必然有原因
收錄日期: 2021-04-26 13:14:40
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20090410000051KK01486