Saturday, December 5, 2009

Problem 398: Parallelogram, Area, Similarity, Congruence

Proposed Problem
Click the figure below to see the complete problem 398 about Parallelogram, Area, Similarity, Congruence.

Problem 398: Parallelogram, Area, Similarity, Congruence.
See also:
Complete Problem 398
Level: High School, SAT Prep, College geometry

Posted by Antonio Gutierrez at 4:33 PM
Labels: , , , ,

2 comments:

  1. c.t.e.oDecember 7, 2009 at 1:13 PM

    suggest to others

    MN mark as x. Express EM and NC by x (thales theorem)
    Express h1 (altitude EBC, or AFD) by h2 (altitude AECF)
    (similar triangles)
    Express S=s1+s2+s3 (s1 EBC, s2 AECF, s3 AFD)

    ReplyDelete
  2. Peter TranJuly 14, 2010 at 10:15 AM

    Let S2= Area(BHDG)
    We have NG=HQ=2/3 *PD [Tri. AQH~Tri. APD]
    NP=1/2* PD [Tri. DPF~ Tri. DNC]
    So NG/NP=4/3

    Calculate DG/NP= (PD+NP+NG)/NP= 2+1+4/3=13/3
    S1/S2=Area(MNPQ)/Area(BHDG)=NP/GD =3/13 [Both para. have the same height]
    S2/S= Area(BHDG)/Area(ABCD)= DH/DA=1/3 [Both para. have the same height]

    So S1/S=1/13

    Peter Tran
    vstran@yahoo.com

    ReplyDelete

Subscribe to: Post Comments (Atom)