Question
Sun July 15, 2012 By: Gaurav

Prove that if two sides of an angel are perpendicular to the sides of another angel. Then the angels are either equal or supplementary.

Expert Reply
Mon July 16, 2012
 
Answer : Given :  two sides of an angel are perpendicular to the sides of another angel.
To prove : the angels are either equal or supplementary.
 
Let AB perpendicular to BE and AD to DE.
 
Now, we know that in traingle ABC and CDE 
Angle ABC = angle CDE = 90 degrees   { given }
Angle ACB = angle DCE { opposite angles are equal}
=> traingle ABC and CDE are similar 
=> angle BAC = angle CED
 
By the property of similar triangles , we can say that ,
they both are acute angles forming a supplementary angles .
Hence proved . 
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