tag:blogger.com,1999:blog-6933544261975483399.post7030261195290192803..comments2024-03-26T19:10:02.918-07:00Comments on Go Geometry (Problem Solutions): Problem 15: Triangle, Cevian, Angles, CongruenceAntonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger11125tag:blogger.com,1999:blog-6933544261975483399.post-63952155880735375962019-03-18T07:38:41.014-07:002019-03-18T07:38:41.014-07:00Construct point E on the left of AC such that AE=A...Construct point E on the left of AC such that AE=AB. Verily, EBC is isosceles, and so is BAE. Now, 3x=120 --> x=40.Ercan Cemhttps://www.blogger.com/profile/17715448112482768479noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-21354900884846344302019-03-04T05:58:41.832-08:002019-03-04T05:58:41.832-08:00Great proof by rv !Great proof by rv !Greghttps://www.blogger.com/profile/14941282981782772132noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-74529385158097308662019-02-25T10:57:06.788-08:002019-02-25T10:57:06.788-08:00See original solution on this video<a title="See the video" href="https://youtu.be/8Zn_SxeWuzU" rel="nofollow"> See original solution on this video</a><br />rv.littlemanhttps://www.blogger.com/profile/05572092955468280791noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-25527116447644234042019-02-22T09:24:22.182-08:002019-02-22T09:24:22.182-08:00See original solution on this video<a title="See the video" href="https://youtu.be/6EZvMsDnicg" rel="nofollow"> See original solution on this video</a><br />rv.littlemanhttps://www.blogger.com/profile/05572092955468280791noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-57276977153709678032017-07-28T20:21:28.613-07:002017-07-28T20:21:28.613-07:00Construct point E, which lies on AB extended, such...Construct point E, which lies on AB extended, such that AE=AD. Join AE and DE.<br />Triangle BED and BCD are congruent (SAS)<br />Hence <BED=x <br />Since AE=AD,<br /><ADE=x<br />So <BAD=2x<br />By angle sum of triangle in ABC,<br />x=(180-30-30)/3<br />x=40Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-39091163762178707762016-10-15T09:01:07.298-07:002016-10-15T09:01:07.298-07:00https://www.youtube.com/watch?v=Rg1AM58ShnEhttps://www.youtube.com/watch?v=Rg1AM58ShnEgeoclidhttps://www.blogger.com/profile/07989522895596673545noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-28039707538466239062015-07-20T04:50:48.621-07:002015-07-20T04:50:48.621-07:00Extend BA to F such that BF = BC. Hence Tr. FBC is...Extend BA to F such that BF = BC. Hence Tr. FBC is equilateral and both Tr.s FAD & FDC are isoceles since BD is the perpendicular bisector of FC<br />So from Tr. FDC 60-x= 60-A/2 and so x= A/2, which can only happen when A= 80 and x=40 since B= 60<br /><br />Sumith Peiris<br />Moratuwa<br />Sri LankaSumith Peirishttps://www.blogger.com/profile/06211995240466447227noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-57656357691266847562012-04-15T04:47:43.583-07:002012-04-15T04:47:43.583-07:00The solution is uploaded to the following link:
h...The solution is uploaded to the following link:<br /><br />https://docs.google.com/open?id=0B6XXCq92fLJJMk52SXpZdlZFRFUAnonymoushttps://www.blogger.com/profile/07812499400423119847noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-47433035257543092422010-10-04T20:05:35.209-07:002010-10-04T20:05:35.209-07:00Let E be a point on BC with BE=BA. Since BA=BE an...Let E be a point on BC with BE=BA. Since BA=BE and ang(ABE)=60 deg,triangle BAE is an Equilateral triangle and DA=DE=EC. Hence we see that ang(DCE)=x=ang(CDE) and ang(DEA)=x/2 and hence 2x=x/2+60, that is , x=40 degree.bae deok rak(bdr@korea.com)noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-83612400592560829932010-07-02T02:56:10.660-07:002010-07-02T02:56:10.660-07:00http://ahmetelmas.files.wordpress.com/2010/05/cozu...http://ahmetelmas.files.wordpress.com/2010/05/cozumlu-ornekler.pdfAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-74764183765364186112009-03-17T00:54:00.000-07:002009-03-17T00:54:00.000-07:00Extend BA to point E such that AE=AD. Now,AB+AD = ...Extend BA to point E such that AE=AD. Now,<BR/>AB+AD = AB+AE = BE. But BC=AB+AD. Hence BE=BC. In triangles EBD & CDB, AD is common, the included angles ABD & DBC are each = 30 and BE=BC which makes the triangles congruent. Thus angle AED = x and angle ADE also =x since AD=AE by construction while angle BAD=x+x=2x and sngle ADB=x+30. Triangle ABD now gives, 30+2x+30+x=180 so x=40 deg.<BR/>Ajit: ajitathle@gmail.comAjithttps://www.blogger.com/profile/00611759721780927573noreply@blogger.com