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### Course: Geometry (all content)>Unit 2

Lesson 7: Angles between intersecting lines

# Proving angles are congruent

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

## Want to join the conversation?

• 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?)
• Both propositions can be proved by Euclid's fifth postulate, an axiom in Euclidean geometry.
• 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.
• Can't you just use alternate interior angles which would be a lot simpler?
• That's a good strategy indeed:D.
why i havent thought this earlier?*-*
(1 vote)
• 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.