2002 AMC 10A Problems/Problem 20
From AoPSWiki
Problem
Points 
and 
lie, in that order, on 
, dividing it into five segments, each of length 1. Point 
is not on line 
. Point 
lies on 
, and point 
lies on 
. The line segments 
and 
are parallel. Find 
.
Solution
As 
is parallel to , angles FHD and FGA are congruent. Also, angle F is clearly congruent to itself. From SSS similarity, 
; hence 
. Similarly, 
. Thus, 
.
See Also
| 2002 AMC 10A (Problems • Resources) | ||
| Preceded by Problem 19 | Followed by Problem 21 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
