Couldn't you prove this faster by saying MLK and NLJ are similar, as they have two angles with the same measure (C and the 90° angle), and all angles in similar triangles are equal?

yes but that is what sal is trying to explain in this video. It as all nice that you can say that as they have two angles with the same measure and all angles in similar triangles are equal but sal was showing mathematically why you are able to say that.

why do you have to prove they are congruent?

So that you can tell if they are congruent or not, before moving on the the new step in geometry.

Forgive me if this is specified within the video, but how did Sal know that all of the interior angles equal 180 when put together in a triangle?

The sum of the angles of a triangle is equal to 180°.

Is there a way to find the actual degrees of angles a and c without using a protractor?

In trigonometry, you can find angle measures based on how steep they are. Every steepness has a different angle associated with it.

wouldn't an easier proof be to simply say that both triangles share angle c and both have a 90-degree angle, meaning the final angle for both has to be 180-90-c?

Yes, and that is essentially what is shown in this video, though explained more thoroughly.

so the sides of a right triangle equal 90 degrees, and the angles equal 180?

Several issues with your question, sides of a triangle are never measured in degrees, they are measured in units (including units, feet, meters, etc.) and there is no specific measurement unless you are given a particular right triangle. The only thing for sure about the sides of a right triangle is that the Pythagorean Theorem (a^2 + b^2 = c^2) will always work. The two acute angles of a right triangle are complementary (add to be 90 degrees) which does mean that there are 180 degrees in a right triangle, but this can be generalized to any triangle.

I don't really understand the point of this video. We already know that vertical angles in transversals are also congruent but what was the point of this video? To prove that a=b and how?

The point of the video is about Sal proving that two angles are congruent in a really interesting triangle like figure.

how do you do a negative parallel problem? none of us can figure it out.

What do you mean by that? Are you simply asking how to find parallel lines that have negative slopes?

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Geometry (all content)

Course: Geometry (all content) > Unit 2

Lesson 7: Angles between intersecting lines

Proving angles are congruent

Name: Proving angles are congruent
Uploaded: 2015-03-27T16:17:40Z
Description: Sal proves that two angles are congruent in a really interesting triangle like figure.

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Sal proves that two angles are congruent in a really interesting triangle like figure.

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Alexander Kokin
Posted 8 years ago. Direct link to Alexander Kokin's post “It may seem like a proof ...”
It may seem like a proof for corresponding angles formed by an intersection of two parallel lines are equal. However, as far as I remember, we use corresponding angles are equal to prove that the sum of angles in a triangle is equal to 180 (the fact that is used in this video). Is it a vicious circle?)
Button navigates to signup pageComment on Alexander Kokin's post “It may seem like a proof ...”
(23 votes)
Answer
- Quan QIU
  Posted 3 years ago. Direct link to Quan QIU's post “Both propositions can be ...”
  Both propositions can be proved by Euclid's fifth postulate, an axiom in Euclidean geometry.
  Button navigates to signup page
  (1 vote)
T#1EH
Posted 8 years ago. Direct link to T#1EH's post “Couldn't you prove this f...”
Couldn't you prove this faster by saying MLK and NLJ are similar, as they have two angles with the same measure (C and the 90° angle), and all angles in similar triangles are equal?
Button navigates to signup pageButton navigates to signup page
(6 votes)
Answer
- Shadow
  Posted 8 years ago. Direct link to Shadow's post “yes but that is what sal ...”
  yes but that is what sal is trying to explain in this video. It as all nice that you can say that as they have two angles with the same measure and all angles in similar triangles are equal but sal was showing mathematically why you are able to say that.
  Comment on Shadow's post “yes but that is what sal ...”
  (4 votes)
Arav
Posted 7 years ago. Direct link to Arav's post “why do you have to prove ...”
why do you have to prove they are congruent?
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(5 votes)
Answer
- Thien D Ho
  Posted 7 years ago. Direct link to Thien D Ho's post “So that you can tell if t...”
  So that you can tell if they are congruent or not, before moving on the the new step in geometry.
  Comment on Thien D Ho's post “So that you can tell if t...”
  (3 votes)
airsquared
Posted 5 years ago. Direct link to airsquared's post “Can't you just use altern...”
Can't you just use alternate interior angles which would be a lot simpler?
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(4 votes)
Answer
- Snakeeyes
  Posted 4 years ago. Direct link to Snakeeyes's post “That's a good strategy in...”
  That's a good strategy indeed:D.
  why i havent thought this earlier?*-*
  Button navigates to signup page
  (1 vote)
Kira
Posted 5 years ago. Direct link to Kira's post “Forgive me if this is spe...”
Forgive me if this is specified within the video, but how did Sal know that all of the interior angles equal 180 when put together in a triangle?
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- WeiWei4834
  Posted 5 years ago. Direct link to WeiWei4834's post “The sum of the angles of ...”
  The sum of the angles of a triangle is equal to 180°.
  Comment on WeiWei4834's post “The sum of the angles of ...”
  (4 votes)
James Oh
Posted 7 years ago. Direct link to James Oh's post “Is there a way to find th...”
Is there a way to find the actual degrees of angles a and c without using a protractor?
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- olesullivan
  Posted 7 years ago. Direct link to olesullivan's post “In trigonometry, you can ...”
  In trigonometry, you can find angle measures based on how steep they are. Every steepness has a different angle associated with it.
  Button navigates to signup page
  (3 votes)
Tommi Rossi
Posted 7 years ago. Direct link to Tommi Rossi's post “wouldn't an easier proof ...”
wouldn't an easier proof be to simply say that both triangles share angle c and both have a 90-degree angle, meaning the final angle for both has to be 180-90-c?
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- kevin.luchua
  Posted 7 years ago. Direct link to kevin.luchua's post “Yes, and that is essentia...”
  Yes, and that is essentially what is shown in this video, though explained more thoroughly.
  Button navigates to signup page
  (2 votes)
Tova Grossman
Posted 5 years ago. Direct link to Tova Grossman's post “so the sides of a right t...”
so the sides of a right triangle equal 90 degrees, and the angles equal 180?
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(2 votes)
Answer
- David Severin
  Posted 5 years ago. Direct link to David Severin's post “Several issues with your ...”
  Several issues with your question, sides of a triangle are never measured in degrees, they are measured in units (including units, feet, meters, etc.) and there is no specific measurement unless you are given a particular right triangle. The only thing for sure about the sides of a right triangle is that the Pythagorean Theorem (a^2 + b^2 = c^2) will always work.
  The two acute angles of a right triangle are complementary (add to be 90 degrees) which does mean that there are 180 degrees in a right triangle, but this can be generalized to any triangle.
  Button navigates to signup page
  (2 votes)
Hamad Chughtai
Posted 5 years ago. Direct link to Hamad Chughtai's post “I don't really understand...”
I don't really understand the point of this video. We already know that vertical angles in transversals are also congruent but what was the point of this video? To prove that a=b and how?
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- Charush M
  Posted 5 years ago. Direct link to Charush M's post “The point of the video is...”
  The point of the video is about Sal proving that two angles are congruent in a really interesting triangle like figure.
  Button navigates to signup page
  (2 votes)
Tim Connor
Posted 6 years ago. Direct link to Tim Connor's post “how do you do a negative ...”
how do you do a negative parallel problem? none of us can figure it out.
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- David Severin
  Posted 6 years ago. Direct link to David Severin's post “What do you mean by that?...”
  What do you mean by that? Are you simply asking how to find parallel lines that have negative slopes?
  Button navigates to signup page
  (2 votes)

Video transcript

We have an interesting looking diagram here. Let's see if we know a few things about this diagram. Let's say we know that line MK is parallel to line NJ. So this line is parallel to this line. This is line MK, this is line NJ. Now, given that and all the other information on this diagram, I'm hoping to prove that the measure of this angle LMK is equal to the measure of this angle over here and this angle is LNJ. Another way of writing this is; the measure of LMK is b and the measure of LNK is a. So we want to prove that b is equal to a using all this information that we know. Like always I encourage you to try this on your own before I walk through it. Alright, let's walk through it. The first thing you might see is I have a triangle formed up here, triangle MLK. What do we know about the measurement of the interior angles of a triangle? The measures of the interior angles of a triangle are going to add up to 180 degrees. We know that b, which is the measure of this angle plus the measure of this angle, c plus the measure of this right angle, which is plus 90 degrees is going to be equal to 180 degrees. And so if we subtract 90 degrees from both sides we're going to get b plus c is equal to 180 degrees minus 90 degrees. It's going to be 90 degrees. Or if we wanted to solve explicitly for b we could subtract c from both sides, and we could write b is equal to 90 degrees minus c. So that's interesting, that's one way of expressing b. Can we express a in a similar way? Once again, if at any point you get inspired I encourage you to do that. If we look carefully we see that we have triangle NLJ, this really big triangle, it's really most of the diagram. What's interesting about NLJ is that J is another right triangle, c is one of the measures of one of the interior angles, and a is a measure of the other interior angle. We can write something very similar, we can write a plus c plus 90 degrees is going to be equal to 180 degrees. So what can we do here? We can do the exact same process to solve for a. If we subtract 90 from both sides and we subtract c from both sides what do we get? We get a is equal to 90 degrees and if you subtract c from both sides you're going to get 90 degrees minus c. Now this is interesting, b is equal to 90 degrees minus c and a is equal to 90 degrees minus c. So 90 degrees minus c is equal to a, it's also equal to b. Or, we can now say that a must be equal to b, that the measure of angle LMK which is b is equal to the measure of angle LNJ which is equal to a.