If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## Geometry (all content)

### Course: Geometry (all content)>Unit 2

Lesson 7: Angles between intersecting lines

# Parallel lines & corresponding angles proof

Proof by contradiction that corresponding angle equivalence implies parallel lines. Created by Sal Khan.

## Want to join the conversation?

• I don't get how Z= 0 at •  Z is = to zero because when you have
x+180-x+z=180
you can cancel out the +x and -x leaving you with
180+z=180
if you subtract 180 from both sides you get
z=0
• Imho the videos (actually there are more of them but they all resort to the same reasoning) about transversals and the ones about the sum of the angles inside a triangle are not consistent because they are circular reasoning : the "sum of angles in a triangle" starts from alleged proof of "angles in parallel lines and transversals", while these video's don't prove anything (it's taken for granted) in a rogorous manner; the only proof is the proof "ad absurdum" in this video, and this assumes a proven "sum of angles in a triangle". To me this is circular reasoning, and therefore not valid.

Basically, in these two videos both postulates are hanging together in the air, and that's not what math should be.

I say this because most of the things in these videos are obvious to me; the way they are (rigourously) built from the ground up isn't anymore (I'm 53, so that's fourty years in the past) ;) • It's not circular reasoning, but I agree with "walter geo" that something is still missing.

Assumption:
- sum of angles in a triangle is constant, which assumes that if l || m then x = y
To prove:
- if x = y, then l || m

Now this video only proved, that if we accept that
if l || m then x=y is true
THEN
if x=y then l || m can be proven

A proof is still missing. Let's say I don't believe that if l || m then x=y. Then it's impossible to make the proof from this video. One might say, "hey, that's logical", but why is more logical than what is demonstrated here?
• I did not get Corresponding Angles 2 (exercise). The video has helped slightly but I am still confused. Could someone please explain this? • If parallel lines are cut by a transversal (a third line not parallel to the others), then they are corresponding angles and they are equal, sketch on the left side above. We know that angle x is corresponding to angle y and that l || m [lines are parallel--they told us], so the measure of angle x must equal the measure of angle y. so if one is 6x + 24 and the other is 2x + 60 we can create an equation: 6x + 24 = 2x + 60. that is the geometry part....now the algebra part: 6x + 24 = 2x + 60 [I am recalling the problem from memory]
using algebra rules i subtract 24 from both sides
6x + 24 - 24 = 2x + 60 - 24 and get 6x = 2x + 36.
NEXT if 6x = 2x + 36 then I subtract 2x from both sides
6x - 2x = 2x - 2x + 36 and get 4x = 36
if 4x = 36 I can then divide both sides by 4 and get x = 9
It might be helpful to think if the geometry sets up the relationship, the angles are congruent so their measures are equal, from the algebra; once we know the angles are equal, we apply rules of algebra to solve. let me know if this helps:
Thank you • so z means zero. wat about x? wat deos it equal?
thnk u • What does he mean by contradiction in ?
(1 vote) • in -
what does he mean by zero length • He basically means: look at how he drew the picture. The length of that purple line is obviously not zero. But then he gets a contradiction. For x and y to be equal AND the lines to intersect the angle ACB must be zero. For such conditions to be true, lines m and l are coincident (aka the same line), and the purple line is connecting two points of the same line, NOT LIKE THE DRAWING. This is the contradiction; in the drawing, angle ACB is NOT zero. But for x and y to be equal, angle ACB MUST be zero, and lines m and l MUST be the same line.
• So, how do you prove lines parallel? Like the whole t-chart way.   