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.

### Course: Geometry (all content)>Unit 13

Lesson 6: Trigonometric ratios and similarity

# Trig challenge problem: verify identities

Sal is given a diagram with multiple right triangles and is asked to verify identities relating to trig ratios in those triangles. Created by Sal Khan.

## Want to join the conversation?

• At about , why are not EF = DC? The other angle in all the other triangles is 59, so they are similar triangles... I thought the ratios of the sides of similar triangles were consistent... Am I right?
• The triangles may be similar, but the definition of similar is having angles that are the same. Sal said that the ∆FEG could be enormous-- we cannot tell the scale. So the lines aren't the same distance.

You were right about the triangles being similar, but in order for the sides to equal each other, the triangle has to be congruent. To tell that, we would need to have one more piece of information; a side length on both.

The reason for this (just in case) is that in order to find congruence of triangles, we need three pieces of information, either on angles or sides. But if we have three angles, it's redundant, since we can calculate one from the other two. So we need at least one side in order to be able to find congruence.
• so on a right triangle the hypotenuses is the only side that does not touch the right angle?
• That's right. It is the longest side and it is opposite the right angle.
• At he says there's no evidence that DC is equivalent to AC. Are we sure? How do we know DC is not AC? Is it bigger or smaller or what?
• We know triangle ADC is congruent to triangle CBA, because of AAS congruence postulate, so we know DC is equal to AB. AB does not equal to AC, because measure of angle ABC and angle ACB are not 45 degrees each (which means triangle CBA is not isosceles). So, we know DC (which equals to AB) does not equal to AC.
• This is to anyone at all, does it really matter how you label the sides?For instance instead of AC it's CA or CB it's BC
• No,It Doesn't Make Any Difference...
Whether It's AC Or CA...
As The Lengths Are Perfectly Same...
• I've heard Sal use the term "arbitrary" quite a few times. What does this exactly mean? Example: of this video.
• It just means "based on random choice". In other words, when Sal chooses an "arbitrary function" or an "arbitrary number", it just means that he is choosing those things randomly, for no particular reason.
• Wait isn't triangle acd and triangle abc simiar and the one side they share is equal so they are to scale and are congruent as all other sides have to be equal (they share ac so are equal lengths)
• They are similar, but you would have to do extra work to prove they are congruent, and we only need to know they are similar to complete this problem.
• What does the letter 'm' means?
• It basically stands for 'measure'. So m∠(ABC) is saying the measure of angle(ABC). It refers to how many degrees that angle is.
• I have really bad internet connection, so the rest of the video (after Sal expains the problem) isn't loading. What is the final answer?
I would recommend not 2 take a second hand phone suchaeta:)
• I understand this problem however when I practice on the corresponding module I encounter questions that are unlike this problem, and seem to hit a brick wall of frustration. Are there any additional video examples of problems in this category, and if not can some kind soul please send me a link to their location? Thanks!
• If you're still stuck, can you give an example of one of the problems you're having trouble with?