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## Geometry (all content)

### Course: Geometry (all content)>Unit 12

Lesson 2: Introduction to triangle 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."
• 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?
(1 vote)
• 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.
• I don't understand one thing. Sal already proved that there are two corresponding angles which are congruent. Why bother drawing another set of parallel lines to prove that the third corresponding angles are also congruent?
• What does transversal mean?
(1 vote)
• Trans means across, so in Geometry, a transversal is a line that intersects (or goes across) two or more other lines
• from to in the video i don't get the corresponding angles?
(1 vote)
• In order for two triangles (or other polygons) to be congruent or similar, the two triangles must have 3 sets of congruent angles, If they are the same, then each angle on one triangle must have an angle on the other that corresponds (or matches) it.
• In the Proving Slope is Constant Using Similarity video, the pink/pink side ratio is the same as green/green side ratio. However, you showed that the pink/green ratios are the same. How did you conclude that? It is not explained clearly in the video. Please explain.