How can I prove the betweenness of the tree straight segments

Asked Sep 19 '18 at 08:38

Active Sep 19 '18 at 08:50

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I come across an elementary geometry problem as following:

Assume that $\angle CAD=12°, \angle CBD=24°, \angle CAB=36°, \angle ABD=48°.$ Estimate that $\angle ACD=?$ And I tried so far: Construct along the straight segment $AC$ an equilateral triangle $\Delta ACG.$ And if I know that $CD$ is between $AC$ and $CG,$ then I can estimate that $\angle ACD=30°.$ But I was totally stuck---How can I prove that $CD$ is indeed between $AC$ and $CG?$

edited Sep 19 '18 at 08:50

asked Sep 19 '18 at 08:38

azc

1,259

If $ACG$ is equilateral, how did you get $\angle ACG=30$? – 5xum Sep 19 '18 at 08:42
@5xum: I can prove $\Delta CDG\cong \Delta CDA,$ provided my question above is solved. And then, it is easy to show the desired result. – azc Sep 19 '18 at 08:48
But $\angle ACG$ is one angle of an equilateral triangle, so $\angle ACG=60$! – 5xum Sep 19 '18 at 08:49
@5xum: Sorry, I have made a typo. – azc Sep 19 '18 at 08:51

How can I prove the betweenness of the tree straight segments

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