Question

Can anybody help me with this?

Answer 1

What?

Answer 2

You can start with the given.

Answer 3

How do you prove two lines are parallel?

Answer 4

<5 congruent to <6 and <6 congruent to <4

Answer 5

Can you help me continue? @mathstudent55

Answer 6

You can write those two statements. The reasons are "Given."

Answer 7

I did that. thanks. what could I do next?

Answer 8

If lines m and n are parallel, then angles 1 and 2 are congruent.
If angles 1 and 2 are congruent, then lines m and n are parallel.
You need the second postulate to prove lines parallel.

Answer 9

Since angle 5 is congruent to angle 6, and angle 6 is congruent to angle 4, can you conclude anything about angle 5 and angle 4?

Answer 10

they are also congruent?

Answer 11

Right.

Answer 12

That is your next statement.
<5 is congruent to <4
The reason is "transitive property of congruence"

Answer 13

thank you so much!!!

Answer 14

Now look at the figure above. If angle 1 is congruent to abngle 2, then lines m and n are parallel. Angles 1 and 2 are called alternate interior angles. A theorem states: If two lines are cut by a transversal such that alternate interior angles are congruent, then the lines are parallel.

Answer 15

Sorry in the first sentence you wrote angle 5 and 5?

Answer 16

In your case, angles 4 and 5 are congruent. Angles 4 anf 5 are alternate interior angles, so lines AD and BC are parallel.
Your last statement is
line AD is parallel to line BC
Reason: If two lines are cut by a transversal such that alternate interior angles are congruent, then the lines are parallel.

Answer 17

I fixed it.

Answer 18

Thank you so much!!!!!!!!!!!

Answer 19

wlcm