tag:blogger.com,1999:blog-6933544261975483399.post8242167820539739759..comments2024-03-26T19:10:02.918-07:00Comments on Go Geometry (Problem Solutions): Problem 553: Quadrilateral, Angles, SumAntonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-6933544261975483399.post-67364852786472958072010-12-26T21:01:04.779-08:002010-12-26T21:01:04.779-08:00Join AC.
Let measure angle CAD=x and measure angle...Join AC.<br />Let measure angle CAD=x and measure angle DCA=y<br />Hence ,measure angle BAC=a-x and measure angle BCA=c-y<br />In triangle ABC,by exterior angle theorem,<br />b=(a-x)+(c-y)...(1)<br />and in triangle ACD,<br />d=x+y...(2)<br />Hence, b+d=[(a-x)+(c-y)]+[x+y]<br /> b+d=a-x+c-y+x+y<br /> b+d=a+c.<br />Thus proved.Neha Prabhunenoreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-53366293157101305532010-12-24T12:38:44.676-08:002010-12-24T12:38:44.676-08:00extend BC to E, E on AD
b = a + CED
c = d + CED
=&...extend BC to E, E on AD<br />b = a + CED<br />c = d + CED<br />=> b + d = a + cc .t . e. onoreply@blogger.com