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## Get ready for Algebra 2

### Course: Get ready for Algebra 2>Unit 5

Lesson 3: Ratios in right triangles

# Using similarity to estimate ratio between side lengths

When two right triangles share an acute angle measure, the ratios of the corresponding side lengths within the triangles are equal.  Created by Sal Khan.

## Want to join the conversation?

• Is there a easier way to do this? There are questions on the practice that Sal does not explain. Maybe cousin Fal could explain to me.
• Not that I know of!
• At what did Sal mean when he said "We can take the ratio across triangles"?
• It just means you can create a ratio (think of it in fraction form) of similar sides from one triangle to the other.
• This is HARD!! Any help?
• I would help you but I'm not sure what it is that you need help with. For starters, Sal chose the triangle that he chose because it was the only triangle with similar angles. Angles are everything with trig. You want to pay attention to the angles that the triangle has to see if they are similar. Then, once you can see the corresponding angles, you can find the corresponding sides. After that, sal just divided the numbers for those corresponding sides to find the ratio. Take deep breaths! You got this.
• At , why did Sal choose triangle 2 to approximate the ratio of PN over MN and not triangle 1 or triangle 3 to approximate the ratio of PN over MN?
• For similar triangles, the angles must be the same. So triangle 2 matches the 35-55-90 angles.
• so, since all of the angles added together have to equal 180 and there is always one 90 degree angle, can one angle be like 89 degrees and the other 1 degree or is that not how this works?
• That's absolutely how this works. A 1-89-90 triangle would be very long and narrow, but still be a valid triangle.
• does the square let you know it's a right angle ?
• yes it is a symbol for 90 degrees.
• Can someone help? there are a few questions on the practice that Sal does not explain. I really need help with this And i don't really understand how to do this.
• If two corresponding sides of two triangles are equal, can they be called similar? Or is it important for two corresponding angles to be equal?
(1 vote)
• Similar triangles are based on proportional relationships between the side, and only if the constant of proportionality is one will sides be equal (and then you use the proofs for congruent triangles which are SSS, SAS, ASA, SSA, and HL). If you talk about proportional sides for similar triangles, the proofs are AA, SSS, and SAS. So the question should be if two ... are proportional, can they ...
None of these allow for only two sides, but you do have two sides and the angle between them. The problem with having only two corresponding sides is that the angle between them can create an infinite number of non-similar figures.