Freshman math questions have me stumped.. help?

Question

1. Points D, E, and F are collinear with E between D and F. DE= 15, EF = x+17, and DF = 3x - 10. Find EF and DF.

2. Describe how equality and congruence are used to describe two line segments and their lengths.

3. Line MN and PQ intersect at point E. Name two sets of three collinear points.

Answer 1

1.collinear- on the same line

They're all on one line like this

----D----(length of 15)-----E---(length of x +17)------F---- (the whole thing is 3x-10)  You're going to have to solve for x, but I'll let you figure out the rest ;D

3. see definition of collinear

Answer 2

1. ok....

first, you know DE + EF = DF, DE = 15, EF = x + 17, and DF = 3x - 10. So....

15 + x + 17 = 3x - 10       combine like terms

x + 32 = 3x - 10         bring all like terms together

42 = 2x

x = 21

2. Congruent line segments would have to be of the same length. And I'm pretty sure equal ones would, too. I think that's it.

3. You have some good info here:

The line that goes through M and N also goes through E.

Similarly, the line that goes through P and Q also goes through E.

So you know that M, N, and E are colinear.

You also know that P, Q, and E are colinear.

That's your answer.