Question

Fill in the blanks in the proof. Don’t forget the missing angle in step 3. (2 points per blank)
Given x // t,
Prove: k // w

Answer 1

@Michele_Laino Could you help me with this one?

Answer 2

x \(//\) t, is given

Answer 3

I know thats the given Im just confused on how to fill in the rest of the blanks?

Answer 4

we can say that angles \(1\) and \(14\) are congruent, and angles \(4\) and \(15\) are congruent too, since they are both alternate interior pairs of angles

Answer 5

So then it would look like this?

Answer 6

no, please you have to write that statment using only one row

Answer 7

Ohhh Okay hold on

Answer 8

Like this?

Answer 9

yes! correct!

Answer 10

So for the next line would I say 5,8,9,10 are congruent angles?

Answer 11

for the same reason, we can say that angles \(5\), and \(9\) are congruent, and angles \(8\) and \(10\) are congruent too

Answer 12

Okay so this all makes sense. I just don't get what I would put for substitution on the next line?

Answer 13

yes! correct! since we can write this:
angles \(5\) and \(1\) have to be congruent, angles \(14\) and \(9\) have to be congruent
angles \(8\) and \(4\) have to be congruent, and angles \(10\) and \(15\) have to be congruent, for the uniqueness of alternate interior angles

Answer 14

so, we can do the subsequent substitutions:
5=1, 9=14
8=4, and 10=15

Answer 15

@Michele_Laino Okay that makes total sense! and so for the last line would be put "Proven" for the reason?

Answer 16

the reason is "uniqueness of alternate interior angles"

Answer 17

Okay thank you so much again for your help! :)

Answer 18

:)

Answer 19

another proof, can be this:
step #2
since x and t are paralell then angles \(14\) and \(9\) have to be congruent, and angles \(3\) and \(7\) have to be congruent
step #3 we can write angles \(7\) and angles \(5\) are congruent since they are vertical angles
step #4, the substitution is:
\(5=1\) and \(9=14\), so being \(3=14\) (since \(3\) and \(14\) are corresponding angles), then we have \(5=9\) and so k \\ w

Answer 20

I think that this second proof is better than the first proof @bobbyjack1200