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### Course: Geometry (FL B.E.S.T.)>Unit 6

Lesson 5: Proving relationships using similarity

# Proof: parallel lines have the same slope

Sal proves that parallel lines have the same slope using triangle similarity.

## Want to join the conversation?

• At , how can you assume that the lines which the vertical transversal passes through are parallel? I know that you claim that they are in the beginning, but what if that information is not given in a problem?
• If the lines are parallel, certainly the exercise will tell you.
• Is this material on the GED test? I teach GED classes to adults. I also was curious of its applications in the world. Thanks!
• in the world there are many times when proving to things are parallel is vital(this being basiclly the idea in the video, even if not said directly):
-archetecture
-mathmatician
engineer
botanist
plastic surgeon
8 year old you likes to play minecraft pocket edition on his moms phone whil wait in the grocery store line.
and many more😉
• Does this have to do with trigonometry?
cause if so it explains why i didn't understand this
• No this is not trigonometry. You can think of this as Algebra I or pre-algebra. They just wanted to show why this is always true
• Sal making me think I had a dead pixel for a moment there.
• what i don't get about this is that he's proving the fact that they have the same slope by the fact that he has the same slope.... isn't that the definition of a parallel line ?

sorry if i'm misunderstanding this. help is appreciated :)
• Two lines are parallel if they lie in the same plane and don't intersect. The definition has nothing to do with coordinate geometry or slopes.

By proving that parallel lines have the same slope, Sal is translating the concept of parallelism from synthetic (non-coordinate) geometry to coordinate geometry.
• Couldn't the slope be negative, and still have the same ratios of sides of right triangles drawn on them?
• Yes, if the right end of the parallel lines had been drawn angled down their slopes would have been negative.
(1 vote)
• Why do we need a video to prove something that seems so incredibly obvious? Lines that have the same slope are parallel, since that's what parallel means, right?
• Because sometimes your intuition is not always true. For example, draw a circle. Then draw a some points on the perimeter of the circle, then connect the points with as many straight lines as possible. Then the question is: What is the maximum number of sections you can get inside the circle? Start small

With 2 dots, it is clear you can get 2 sections
With 3, you can get 4 sections
With 4, you can get up to 8 sections
With 5 dots, you will get up to 16 sections

Without drawing 6 dots n the circle's perimeter, what is the maximum number of sections you can get?