SOLUTION: given: A(2,3), B(5,-1), C(1,0), D(-4,-1), E(0,2), F(-1,-2) prove: angle ABC is congruent to angle DEF

Algebra ->  Length-and-distance -> SOLUTION: given: A(2,3), B(5,-1), C(1,0), D(-4,-1), E(0,2), F(-1,-2) prove: angle ABC is congruent to angle DEF      Log On


   

Question 389081: given: A(2,3), B(5,-1), C(1,0), D(-4,-1), E(0,2), F(-1,-2)
prove: angle ABC is congruent to angle DEF
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Instead of Pythagorean-theorem bashing, I'm only going to find the change in x and y for each pair of points:

(The partial differential operator delta should be uppercase, which represents a total change. Also, I'm taking the absolute value since Pythagorean theorem only depends on the squares of the numbers, regardless of whether change is positive or negative.

A,B
delta%28x%29+=+3
delta%28y%29+=+4

B,C
delta%28x%29+=+4
delta%28y%29+=+1

C,A
delta%28x%29+=+1
delta%28y%29+=+3

D,E
delta%28x%29+=+4
delta%28y%29+=+3

E,F
delta%28x%29+=+1
delta%28x%29+=+4

D,F
delta%28x%29+=+3
delta%28x%29+=+1

We see that AB = DE = 5, AC = DF = sqrt%2810%29, BC = EF = sqrt%2817%29. By SSS, ABC and DEF are congruent triangles.