Geometry Problem
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Level: High School, SAT Prep, College geometry
Thursday, December 23, 2010
Problem 553: Quadrilateral, Angles, Sum
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Geometry Problem
Click the figure below to see the complete problem 553.
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Level: High School, SAT Prep, College geometry
extend BC to E, E on AD
ReplyDeleteb = a + CED
c = d + CED
=> b + d = a + c
Join AC.
ReplyDeleteLet measure angle CAD=x and measure angle DCA=y
Hence ,measure angle BAC=a-x and measure angle BCA=c-y
In triangle ABC,by exterior angle theorem,
b=(a-x)+(c-y)...(1)
and in triangle ACD,
d=x+y...(2)
Hence, b+d=[(a-x)+(c-y)]+[x+y]
b+d=a-x+c-y+x+y
b+d=a+c.
Thus proved.