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## Geometry (all content)

### Course: Geometry (all content) > Unit 11

Lesson 1: Transformations and congruence# Congruent shapes & transformations

If we can map one figure onto another using rigid transformations, they are congruent. They are still congruent if we need to use more than one transformation to map it. They aren't if we use a transformation that changes the size of the shape. Created by Sal Khan.

## Want to join the conversation?

- I'm really having trouble using the reflection tool, especially in the CORAL polygon, instead of coming up diagonally, it starts out vertically and I don't know how to adjust it. Any hints? Many thanks in advance!(26 votes)
- you should be able to do it by moving the two triangles in the middle . Click, hold and rotate with the mouse. then reclick the triangles to perform the action.(21 votes)

- u know, when i was in highschool we used something like

SAS, SSS, AAS and RHS

my question is that could we use that over here??(13 votes)- Yeah those are the main components of congruence(1 vote)

- how do you pronounce congruent(7 votes)
- It pronounced kon-GREW-ent, with the accent on the second syllable (some people put the accent on the first syllable). There is an app in the following link to hear the pronunciation:

http://www.merriam-webster.com/dictionary/congruent(8 votes)

- why do i need to know this in real life?(14 votes)
- scale figures such as blueprints, building circuits on boards, etc.(5 votes)

- How are the two triangles in the video congruent when it looks like they're different shapes? Yes, it is possible to superimpose one onto another but they're not the same shape. One triangle is right triangle and the other is not. How are they congruent? I do not understand.(12 votes)
- Both triangles are right angles, they both have 90 degree angles. It just so happens that the second triangle is rotated. Rotating a triangle does not change any of the angles, meaning it still has a 90 degree angle. If you were to take the corner of a sheet of flat, uncut paper, and put it up to your screen you would see it lines up perfectly with one of the triangle's angles.(7 votes)

- How come those two triangles don't look congruent?(10 votes)
- I was wondering the same thing. No matter how i look at it, or on what device i look at it on, they still don't both look like right triangles...(9 votes)

- Those two shapes are not congruent. The first one has a right angle but the second one doesn't.(10 votes)
- The second one has a right angle, it's just hard to spot.(5 votes)

- Not to be rude but i am just wondering when this will help u in life?(6 votes)
- If you want to build things or be an engineer, then you'll need this. You will need to make things symmetrical and congruent to each other. Take the wheel for example. It needs to be the exact same size otherwise the wheels will turn to the left/right depending on which wheel is smaller. (on one axle)(2 votes)

- So for the postulates, which way do you move around the triangle to figure out the sides and angles? Do you go clockwise around the triangle or counter-clockwise? Does it make a difference? Sorry if this question is confusing...(5 votes)
- Clockwise/counterclockwise don't matter. The only way in which order matters is, for example, the difference between AAS and ASA; in AAS, the congruent side cannot be between the congruent angles. In ASA, the congruent side must be between the congruent angles.(5 votes)

- Why is it important to know the difference between congruent and non-congruent shapes?(0 votes)
- If you are building something, you want it to be congruent to the model you are using. Since Math in one sense is its own language, you need to learn the vocabulary of math.(14 votes)

## Video transcript

- [Instructor] We're
told, "Kason was curious "if triangle ABC and
triangle GFE were congruent, "so he tried to map one
figure onto the other "using a rotation." So let's see, this is triangle
ABC, and it looks like, at first, he rotates
triangle ABC about point C, to get it right over here, so
that's what they're depicting in this diagram. And then they say, "Kason concluded: "It is not possible to map triangle ABC "onto triangle GFE using a sequence "of rigid transformations, "so the triangles are not congruent." So what I want you to
do is pause this video and think about, is Kason correct that they are not congruent,
because you can not map ABC, triangle ABC onto triangle GFE with rigid transformations? All right, so the way I think about it, he was able to do the rotation that got us right over here, so it is rotation about point C, and so this point right over here, let me make sure I get this right, this would've become B prime, and then this is A prime, and then C is mapped to itself,
so C is equal to C prime. But he's not done, there's
another rigid transformation he could do, and that
would be a reflection about the line FG. So if he reflects about the line FG, then this point is going
to be mapped to point E, just like that. And then if you did that,
you would see that there is a series of rigid transformations that maps triangle ABC onto triangle GFE. So Kason is not correct, he
missed one more transformation he could've done, which is a reflection.