1. ## Help with congruency

Let A=(0,0), B=(1,3), and C=(3,3) be points in the Cartesian plane with the max distance Ds={|x1-x2|,|y1-y2|}. Prove that segment AB is congruent to segment AC. Sketch the two segments. Do they look congruent?

My problem: I am not seeing how they are congruent. How can I write a proof if they aren't actually congruent? What am I missing?

2. Originally Posted by ban26ana
Let A=(0,0), B=(1,3), and C=(3,3) be points in the Cartesian plane with the max distance Ds={|x1-x2|,|y1-y2|}. Prove that segment AB is congruent to segment AC. Sketch the two segments. Do they look congruent?
My problem: I am not seeing how they are congruent. How can I write a proof if they aren't actually congruent? What am I missing?
I am assuming that "congruent segments" means that the segments have the same length.
Using the given distance function, do the segments have the same length?

3. I must be understanding the distance function wrong, because I'm getting {1,3} and {3,3}. I know I look so stupid right about now. What am I doing wrong?

4. Originally Posted by ban26ana
I must be understanding the distance function wrong, because I'm getting {1,3} and {3,3}. I know I look so stupid right about now. What am I doing wrong?
.

5. Originally Posted by ban26ana
I must be understanding the distance function wrong, because I'm getting {1,3} and {3,3}. I know I look so stupid right about now. What am I doing wrong?
How can distance be a set? Apply the definition of d you're given:

d_AB = max{|0-1|,|0-3|} = |0-3| = 3

Now do the same with the distance d_AC,a dn if it is the saem as d_AB then AB, AC are congruent, otherwise they aren't.

Tonio

6. Originally Posted by ban26ana
I must be understanding the distance function wrong, because I'm getting {1,3} and {3,3}. I know I look so stupid right about now. What am I doing wrong?
The distance is the larger of the two. The larger of {1, 3} is 3 and the larger of {3, 3} is 3. Those are the same distances so the segments are congurent.

You have "max" misplaced in your first post. it should be "distance Ds= max{|x1-x2|,|y1-y2|}" not "max distance Ds={|x1-x2|,|y1-y2|}"

7. Thank you for explaining that! My professor's first language is not English, and there are a lot of things lost in translation and through the internet. Thanks!