The results for each case of congruence are listed below:
9) Congruent
10) No congruent
11) No congruent
12) Congruent
13) Congruent
14) No congruent
Are two line segments congruent to each other?
There are several ways to determine if two line segments are congruent to each other. One form consists in finding the vector associated with each line segment and the length is found by the Pythagorean theorem:
Now we proceed to show how to apply the vector criterion:
9) AB = (- 4, 8) - (- 4, 5) = (0, 3), CD = (2, 0) - (2, - 3) = (0, 3).
AB = 3, CD = 3. Congruent
10) AB = (1, - 1) - (6, - 1) = (- 5, 0), CD = (4, - 3) - (2, - 3) = (2, 0).
AB = 5, CD = 2. No congruent
11) AB = (- 1, 3) - (8, 3) = (- 9, 0), CD = (5, 3) - (5, 10) = (0, - 7).
AB = 9, CD = 7. No congruent
12) AB = (6, 1) - (6, - 8) = (0, 9), CD = (- 2, - 2) - (7, - 2) = (- 9, 0).
AB = 9, CD = 9. Congruent
13) AB = (- 5, - 1) - (- 5, 6) = (0, - 7), CD = (3, 3) - (- 4, 3) = (7, 0).
AB = 7, CD = 7. Congruent
14) AB = (3, - 4) - (10, - 4) = (- 7, 0), CD = (- 1, 5) - (- 1, 2) = (0, 3).
AB = 7, CD = 3. No congruent
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