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## High school geometry

### Course: High school geometry>Unit 3

Lesson 5: Working with triangles

# Corresponding angles in congruent triangles

We write the letters of congruent triangles so their order tells us which parts are corresponding. In this video, Sal uses this notation to solve some angles. Created by Sal Khan.

## Want to join the conversation?

• At how can we be sure that the three angles equal 180 degrees? It may appear to be a straight line, but without any notation ensuring that it is, how can we be sure?
• Hi J,
Right at the very beginning of the video, at , Sal uses the words "in this larger triangle here" as he outlines triangle ABE. If this was a straight word question however, the question would start out with something like, "Given triangle ABE, prove that ..."
Hope that helps!
• what if it does not give that information? how do you know if they are all congruent or not?
• no sometimes the assignment is to figure out the congruent.
• I may have forgotten from a previous video, but how do you recognize, without a protractor or ruler, what the corresponding angles are? I know they appear when there are two or more congruent triangles, but do you eye them out? Or is their a mathematical way to know. Thanks
• Does the order of how the triangles are written matter?
• Very much so - corresponding angles should match on congruency statements.
For example if we say △ ABC ≅ △ EFG, that tells us a lot about the triangles, ∠ A ≅ ∠ E, ∠B ≅ ∠F, ∠C ≅ ∠G, AB ≅ EF, BC ≅ FG, CA ≅ GE.
• こんいちは！
あのう、わかりません。
Hello!
I do not understand.
I need help with everything.
I have no clue what I'm doing, or what to do.
I struggle with math a lot and I'm not so bright when it comes to math.
• If we know two figures are congruent, then we know matching parts are congruent. So lets use two of the three triangles triangle BCD is congruent to triangle ECD. Letters in the same spot (first, middle, and last) give congruent angles. So <B is congruent to <E, <C is congruent to <C (note they are different angles in the two triangles, but both at vertex C) and <D congrent to <D (once again, two different angles with common vertex). Similarly, matching sides are congruent, so BC congruent of EC (first two letters), CD is congruent to CD (any length is always congrent to itself), and DB is congruent to DE. So given a congruence statement, we can match angles and sides.
• although it's obvious enough to look at it, how do we know that the large shape ABE is definitely a triangle? is there a proof that a shape made of 3 congruent triangles must also be a triangle (and not some extreme quadrilateral where angle ACE could be not 180, but 179.99 degrees or something)?
• Maybe this is a silly question...but is Sal saying that the farthest left triangle is congruent to the two other? If so, could someone please explain why.
Thanks🙂
• it only explains the information given in the question.
• why does ~ on top of = mean congruent
• Don't we need to be given a few more pieces of information? Without being told on the diagram:
Can we actually assume that A, C, and E are colinear?
Same for B, D, and E.
Do we need to assume that C is the midpoint of AE?
Same for D on BE.
And do we need to assume that CD is the altitude of triangle BCE (therefore perpendicular to BE)?
*Edit: Took the word "assume" out of first sentence.