See complete Problem 231 at:
gogeometry.com/problem/p231_triangle_midpoint_transversal_perpendicular.htm
Level: High School, SAT Prep, College geometry
Post your solutions or ideas in the comments.
Friday, January 23, 2009
Elearn Geometry Problem 231: Triangle, Midpoint, Transversal
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join F and D than FD = CE ( middle line ) (1)
ReplyDeletedraw DF" // t than F'F" = d
Tr DFF" and ECC' are similar ( DF // CE )
than
f+d / FD = c / CE from (1)
f+d = c
There are two solutions, depending whether D is above D’ or not
ReplyDeleteSee the drawing
- Define A’ in D’C’ such as AA’ ⊥ D’C’ and B’ such as BB’’ ⊥ D’C’
1) Let suppose D above D’ : b > a
- 2f=a+c
- d=|b-a|/2
- b=c
- d+f=|b-a|/2+(a+c)/2
- 2(d+f)=b-a+a+c=2c
- =>c=f+d
2) Let suppose D under D’ : b < a
- 2f=a+c
- d=|b-a|/2
- b=c
- d-f=|b-a|/2-(a+c)/2
- 2(d-f)=-b+a-a-c=-2c
- =>c=f-d
Complete rectangle FF'C'X
ReplyDeleteTr.s DD'E and FCX are congruent SAS
So CX = d and so c = d + f
Sumith Peiris
Moratuwa
Sri Lanka