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### Course: High school geometry>Unit 3

Lesson 3: Congruent triangles

# Proving triangle congruence

Given a figure composed of 2 triangles, prove that the triangles are congruent or determine that there's not enough information to tell. Created by Sal Khan.

## Want to join the conversation?

• What's the difference between Angle Angle Side and Angle Side Angle?
• Angle Angle Side is when one of the angles is opposite the side.

Angle Side Angle is when both angles are adjacent to the side.
• If the velocity of a raccoon equals the width and height of a chair how does that soccer payer score a goal?
• well, If we know that the chair's angular hypotenuse is divisible by the leg length of the player's chair, we can use the AAAAAASSSASSASSSSSS congruency postulate to conclude that the racoon is doomed to eat trash for the rest of his life.
simple as that.
• Why can't you use the alternate interior angles on the other side to prove congruency? For a better explanation, why isn't angle ACB = DAC?
• Why not? We can always use both alternate interior OR exterior, it's an excellent way, but you should know the variables/measurements. What I mean is that you should have the same variable in both triangles, whether it was a variable or a numerical value. I variables, you can count on 2 x Theta, for 2 congruent angles, in that case, u can prove using these variables. 🙂👍
• why couldn't you use the two congruent sides of AB and DC to use the postulate SAS?
• Because they do not say that segment AB is congruent to segment DC, they only say that they are parallel. As Sal said in the video, you can't say things are congruent just because they look like they are.
• three seconds of silence go crazy
• Can someone please tell me an overview of this?? I am kinda confused. Thanks!
• At around , Sal says that CB and DA are not parallel, or that we couldn't assume as such. But by using the logic that AC is congruent to itself and that DC and AB are congruent, then couldn't we say that CB and DA must also be congruent?

No matter what, in the end there is only one way to connect both sides of the triangle using a straight line. So that would result in both triangles having the same side length, and they must also have the same angle measures. And if they have the same angle measures, in the same spots (because we know 2 side lengths + an angle and where they are), then CB and DA must also be parallel. (We don't need another angle for this, I don't think, but we could easily prove that angle DAC is congruent to ACB, too.)

Right?

Riiight?

I'm not being dumb, am I?
• Merely because two sides of a triangle are congruent does not automatically mean the third side is congruent, it can be in a range of numbers. If one side is 4 and a second is 2, the third side could range fron 4-2<x<4+2. If the two line segments are not parallel, then the third sides would not be congruent.
• The postulate and congruence theorems are the worst part of math. O_O
I have watched so many videos and I still don't get it!
And I absolutely hate word problems, they are my weakness! X(