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標題:

F.3(quadrilaterals)急!

發問:

In the figure,ABCD and AEFG are squares.Prove that∠ABE = ∠ADG. http://s567.photobucket.com/albums/ss118/tony1232_photo/?action=view¤t=math1.jpg

最佳解答:

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)

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Prove AB=AD (given) AE=AG (given) ∠GAE = ∠DAB=90 =>∠GAD+∠DAE = ∠DAE + ∠EAB ==>∠GAD = ∠EAB So ADG~= ABE (SAS) and ∠ABE = ∠ADG