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

Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to view more details of problem 1195.

## Friday, March 4, 2016

### Geometry Problem 1195: Square, Two Rectangles, Congruence, Metric Relations

Labels:
congruence,
metric relations,
rectangle,
square

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http://s28.postimg.org/h7revidfx/Pro_1195_1.png

ReplyDeleteLet u= EA=GK

And v= GE=CJ

Draw JM //BC ( M on AB ,see sketch)

Observe that triangles GKE, JKF, JHC and HGB are similar

And triangle JGK congruent to GJH ( per hypotenuses- legs congruence)

So MG=HJ=GK= u and BM=CJ= v

And GA=u+v=GB => G is the midpoint of AB => GHB is 30-60-90 triangle

So BH= 5.sqrt(3) and CH= 10- 5.sqrt(3) and u= JH=2.CH= 20-10.sqrt(3)

X= DJ=AG+ GM= 5+ u= 25-10.sqrt(3)

From ∆JGK ≡ ∆GJH => MG=GK ?

Deleteplease explain

Draw GM // AD => GMJH cyclic, From GJ diameter => GMJH kite

ReplyDelete=> G midpoint

GB=5, BH=5√3, HC=10-5√3, FD=20-10√3, x=25-10√3