Geometry Problem 1497. Post your solution in the comment box below.

Level: Mathematics Education, K-12 School, Honors Geometry, College.

Details: Click on the figure below.

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Where is Problem 1496?

ReplyDeleteLink: https://gogeometry.com/school-college/5/p1496-triangle-double-angle-isosceles-30-degree-congruence.htm

DeleteTo Antonio : I published solution for this problem few weeks ago . The solution appear in few days then disappear later. I am not sure if there are something wrong in my solution ?

ReplyDeletePeter Tran has left a new comment on your post "Geometry Problem 1497: Scalene Triangle, Transversal, Same Ratio, Proportionality, Isosceles, Double Angle":

Deletehttps://photos.app.goo.gl/vwzCfb5NrWeMwChR6

Problem 1497 solution 2

Draw GK//HC

C, E and K are collinear points => triangles HEC similar to GEK ( case AA)

We have EH/EG=HC/GK=CE/CE => BG=GK

Let BK meet DC at L

Since EH/EG=CE/EK= CF/FB=> BK//EF ( Thales theorem)

We have isosceles and similar triangles GBK and LAB ( case AA)

And ∠ (ALB)= ∠ (ABL)= ∠ (FDC)=alpha

And x= ∠ (HAG)= 2. Alpha

Peter Tran has left a new comment on your post "Geometry Problem 1497: Scalene Triangle, Transversal, Same Ratio, Proportionality, Isosceles, Double Angle":

ReplyDeletehttps://photos.app.goo.gl/LcWs7W3YV9TyGRYW8

Draw BK//HC

H, F and K are collinear points => triangles HFC similar to KFB ( Case AA)

We have CF/BF=HF/FK=CH/BK=CH/BG => BG=BK

Let GK meet DC at L

Since EH/EG=CF/BF=HF/FK => GK//EF ( Thales theorem)

We have isosceles triangles GBK and LAG

And ∠ (ALG)= ∠ (AGL)= alpha

And x= ∠ (HAG)= 2. alpha

Posted by Peter Tran to Go Geometry (Problem Solutions) at Sep 17, 2022, 7:28 PM

My solution, given by the construction of the points E,F may be found at my blog : https://stanfulger.blogspot.com/2022/11/problem-1497-go-geometry.html

ReplyDeleteBest regards,

Stan Fulger