Thursday, December 23, 2010

Problem 553: Quadrilateral, Angles, Sum

Geometry Problem
Click the figure below to see the complete problem 553.

 Problem 553: Quadrilateral, Angles, Sum.
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Level: High School, SAT Prep, College geometry

2 comments:

  1. extend BC to E, E on AD
    b = a + CED
    c = d + CED
    => b + d = a + c

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  2. Join AC.
    Let 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.

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