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

Lesson 5: Proving relationships using similarity

# Proving slope is constant using similarity

Sal uses a clever proof involving similar triangles to show that slope is constant for a line. Created by Sal Khan.

## Want to join the conversation?

• near the end he wrote the ratio A to B as A/B, but I have always been taught to write ratios as A:B, so which one is correct?
• A fraction essentially is a ratio, so you can write it either way
:)
• How would the corresponding angle in a large triangle be the same as one in a smaller one?
• Think of it as a a blue print.... You can express what measurements you need such as, say, 50 feet by 50 feet, but you wouldn't want to draw that big of a shape for a blueprint, so you would scale it down, however it would be understood what the size was by looking at the measurements when you go to build the house or whatever you are building.
• Doesn't concluding that the orange line is a transversal of green parallel lines assume that the orange line has a constant rate of change (for, if the orange line did not have a constant rate of change, then it would not be a transversal and the corresponding angles would not have equal measure)? As such this proof would seem to rely on the conclusion as a premise.
• That's exactly what I was thinking! It's circular logic at its finest and doesn't prove anything. "It has the same slope because in order for it to have the same slope, it has to have the same slope."
• If they are similar, shouldn't the ratio be a/c=b/d, rather than a/b=c/d?
• As in your other question, they are two ways of doing the same thing.
• At wouldn't the ratio be between the two larger sides and the two smaller sides? Like big/big and small/small? I know that I'm wrong how can someone explain that to me?
• If you think about it, they are the same and either way is valid, so neither of you are incorrect. He ended up with a/b = c/d and if you cross multiply you get ad = bc. Doing it your way, you compare a/c = b/d and cross multiplying still gives ad = bc.
• By definition a line has a constant slope. Am I wrong? This proof seems flawed by having the conclusion as one of the arguments.
• You're right. This proof is redundant and unnecessary, as well as not being well phrased. Perhaps there was a point here that we both missed, due to bad explanation or our misunderstanding of the proof, but I doubt it.
• How are we able to use transversals if we are unsure if the line is constant?
• Slopes! I didn't understand slopes when I was learning Algebra I; I don't understand slopes now!