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## #1 2019-02-07 09:40:40

Lauren1415
Member
Registered: 2018-10-17
Posts: 14

### Geometry/parallel lines

I need help with these problems please.
The problems have changes since the last post on this topic

I'm unsure how to upload on image

https://www.compuhigh.net/classes_2/geometry/lesson06/def.jpg

2. Refer to the image . If angle 4 is 70 degrees and angle 6 is 70 degrees, are the lines parallel? Explain.

3. Refer to the image . If angle 2 and angle 6 are both 70 degrees, are the lines parallel? Explain.

Last edited by Lauren1415 (2019-02-07 09:42:01)

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## #2 2019-02-07 12:31:30

Lauren1415
Member
Registered: 2018-10-17
Posts: 14

### Re: Geometry/parallel lines

https://i.imgur.com/0QznckB.gif

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## #3 2019-02-07 13:59:24

Grantingriver
Member
Registered: 2016-02-01
Posts: 115

### Re: Geometry/parallel lines

Hi Lauren1415, for any two parallel lines which are intersected by a third line the symmetrical angles formed by the intersecting line are equal (this result can be proven by Thales's theorem). In the figure which you are providing angle (2) and (6) are symmetrical hence they should be equal if the two lines are parallel and since in the case of question 3 both of them are equal to 70 the two lines are parallel. However, in the case of question 2 we have angle (2)=180-70=110 while angle (6) is 70 therefore the two angles are not symmetrical and hence the pertinent lines are not parallel in this case. I hope that helps.

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