Difference between revisions of "2002 AMC 10A Problems/Problem 20"
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<math>\text{(A)}\ 5/4 \qquad \text{(B)}\ 4/3 \qquad \text{(C)}\ 3/2 \qquad \text{(D)}\ 5/3 \qquad \text{(E)}\ 2</math> | <math>\text{(A)}\ 5/4 \qquad \text{(B)}\ 4/3 \qquad \text{(C)}\ 3/2 \qquad \text{(D)}\ 5/3 \qquad \text{(E)}\ 2</math> | ||
− | [asy] | + | <math>[asy] |
pair A,B,C,D,EE,F,G,H,J; | pair A,B,C,D,EE,F,G,H,J; | ||
A = (0,0); | A = (0,0); | ||
Line 18: | Line 18: | ||
draw(H--C--G--D); | draw(H--C--G--D); | ||
draw(J--EE--G); | draw(J--EE--G); | ||
− | label("<math>A< | + | label("</math>A<math>",A,SW); |
− | label("<math>B< | + | label("</math>B<math>",B,S); |
− | label("<math>C< | + | label("</math>C<math>",C,S); |
− | label("<math>D< | + | label("</math>D<math>",D,S); |
− | label("<math>E< | + | label("</math>E<math>",EE,S); |
− | label("<math>F< | + | label("</math>F<math>",F,SE); |
− | label("<math>J< | + | label("</math>J<math>",J,NE); |
− | label("<math>G< | + | label("</math>G<math>",G,N); |
− | label(scale(0.9)*"<math>H< | + | label(scale(0.9)*"</math>H<math>",H,NE,UnFill(0.1mm)); |
− | [/asy] | + | [/asy]</math> |
==Solution== | ==Solution== |
Revision as of 18:24, 28 November 2015
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 .
ABCDEFJGH
Solution
Solution #1: Since and are parallel, triangles and are similar. Hence, .
Since and are parallel, triangles and are similar. Hence, . Therefore, . The answer is (D).
Solution #2: As is parallel to , angles FJE and FGA are congruent. Also, angle F is clearly congruent to itself. From AA similarity, ; hence . Similarly, . Thus, .
See Also
2002 AMC 10A (Problems • Answer Key • 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 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.