See complete Problem 235 at:
gogeometry.com/problem/p235_parallelogram_transversal_perpendicular_lines.htm
Level: High School, SAT Prep, College geometry
Post your solutions or ideas in the comments.
Tuesday, January 27, 2009
Elearn Geometry Problem 235: Parallelogram, Transversal line, Perpendicular lines
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draw AB" // A'C', B" is point BB' meet it
ReplyDeletedraw DD" // A'C', D" is point DD' meet it
tr ABB" and DCD" are similar ( equal ang between side and perpend)
b+a / AB = c+d / CD
or b+a = c+d
See the drawing
ReplyDelete- A’D’ is the projection of AD on A’C’ and B’C’ if the projection of BC on the same A’C’
- AD=BC=>A’D’=B’C’
- Draw a parallel of AD passing through A’ intersecting DD’ in L
- AA’=D’L=a => D’L=d-a
- Draw a parallel of BC passing through C’ intersecting BB’ in K
- CC’=BK=c => B’K=b-c
- ΔA’D’L is congruent to Δ C’B’K => D’L=B’K
- => d-a=b-c
- Therefore d+c=a+b