Math Help Please help! Would like answers and explanation?

Question

I dont't think its missing anything, I copied it from the practice book exactly. Also They never mentioned having to use grids.

Answer 1

If you can't do this in your head or with a simple drawing, draw the number line (ignore the dots (.) and pretend there is a horizontal line above the numbers):

7.-6.-5.-4.-3.-2.-1.-0.+1.+2.+3.+4.+5....

.......A.........B......C............D

For AB and CD, put your finger on A. Now, as you move it a number at a time to B (-2), count the steps. As you move from from -5 to -4 say "one". Then as you move it from -4 to -3 say "two". Then as you move it from -3 to -2 say "three". So, from -5 to -2 is 3.

Now do the same for C to D, moving from 0 to 3. That requires 3 steps, making it 3. Put them together, AB and CD is 3 and 3 is 6. If they were congruent, they'd be touching or overlapping, and they're not.

Now do the same for AC and BD and for BD and AD. The other two overlap, but just add up the spaces for each one. AC is 5 and BD is 5 to ACandBD is 10, and it's congruent as they overlap.

You can do the last one, I'm counted out and think I'll take a nap.

Have fun.

Answer 2

to show the work for this you would need to draw this on a grid, although your coordinates need another value to do so.  I think you are missing something.

Answer 3

To find the length, just take the right endpoint minus the left endpoint.

1. AB = -2 - (-5) = 3

  CD = 3- 0 = 3

So AB is congruent to CD (same length).

2. AC = 0 - (-5) = 5

BD = 3 - (-2) = 5

So AC is congruent to BD.

3. BD = 5 again.

AD = 3 - (-5) = 8

So BD and AD are not congruent (different lengths).