Question

Determine if statement (3) follows from statements (1) and (2). if it does, state the law that explains why. If it does not, write "invalid".
(1) parallel lines do not intersect
(2) lines m and n are parallel
(3) lines m and n do not intersect

Answer 1

i think its valid by the law of syllogism. is that right or...?

Answer 2

the law of syllogism is a little different.

$$
\Large{
if~p~then~ q \\
if~q~then~ r
\over
if~ p ~then ~r
}
$$

Answer 3

so then it's invalid?

Answer 4

it is valid, but using a different rule

Answer 5

detachment?

Answer 6

yes

Answer 7

thank you!

Answer 8

law of detachment:

$$

\Large{
if~p,~then~ q \\
~~p
\over
q
}




$$

Answer 9

think you can help me with 1 more question?

Answer 10

ok

Answer 11

Write a two-column proof for the following:
given:∠1 and ∠2 form a linear pair and m∠1=2(m∠2)
prove:m∠2=60

Answer 12

sorry, given: angle1 and angle2 form a linear pair and angle1=2(angle2)
prove:angle2=60

Answer 13

i know that a linear pair adds up to 180 degrees, so angles 1 and 2 are supplementary, so 180-120=60, but idk how to write this in proof form. and i have to state the properties/laws that go with each step

Answer 14

can you upload an image of the assignment, it is hard to follow the directions

Answer 15

it's question 9

Answer 16

thanks

Answer 17

<1,<2 linear pair (given)
<1 +<2 = 180 (linear pair are supplementary)
(2*<2) + <2 = 180 (by substitution)
3*<2 = 180 (by algebra)
<2 = 180 / 3 (by algebra)

Answer 18

what do you mean by algebra?

Answer 19

collect like terms

Answer 20

ok ty!

Answer 21

do you see the substitution part, because in the directions <1 = 2* <2

Answer 22

yea

Answer 23

but where did you get the 3*<2 part

Answer 24

<1,<2 linear pair (given)
m<1 +m<2 = 180 (linear pair are supplementary)
2*m<2 + m<2 = 180 (substitution)
3*m<2 = 180 (addition, collect like terms )
m<2 = 180 / 3 (equals divided by equals is equal)

Answer 25

oh i see

Answer 26

ok i got it, thx again!