Congruence postulates
-
Congruent Triangles and SSS
-
SSS to Show a Radius is Perpendicular to a Chord that it Bisects
-
Other Triangle Congruence Postulates
-
Two column proof showing segments are perpendicular
-
Finding Congruent Triangles
-
Congruency postulates
-
More on why SSA is not a postulate
-
Perpendicular Radius Bisects Chord
-
Congruent Triangle Proof Example
-
Congruent Triangle Example 2
-
Congruent triangles 1
-
Congruent triangles 2
Finding Congruent Triangles Using the SSS, ASA, SAS, and AAS postulates to find congruent triangles
⇐ Use this menu to view and help create subtitles for this video in many different languages.
You'll probably want to hide YouTube's captions if using these subtitles.
- What we have drawn over here is 5 different triangles
- What I wanna do in this video is
- figure out which of these triangles are congruent
- to which other of these triangles
- And to figure that out I'm just
- over here, going to write our triangle congruency postulates
- So we know that 2 triangles are congruent
- if all of their sides are the same
- So side, side, side
- We also know they are congruent if we have a side
- and then an angle between the sides,
- and then another side that is congruent
- So side-angle-side
- If we reverse the angles and the sides,
- we know that's also a congruence postulates
- So if we have an angle and then another angle,
- and then the side in between them is congruent,
- then we also have 2 congruent triangles
- And then finally, if we have an angle and then another angle,
- and then a side, then that is also
- Any of these imply congruencies
- So let's see our congruent triangles
- So let's see what we can figure out
- right over here for these triangles
- So right in this triangle ABC over here,
- we're given this length 7, then 60 degrees, and then 40 degrees,
- or another way, think about it
- We're given an angle, an angle, and a side
- 40 degrees, and 60 degrees, then 7
- And in order for something to be congruent here,
- they would have to have an angle-angle side given
- at least, unless we made
- We have to figure it out some other way,
- but I'm guessing for this problem
- Though this already gave us the angles,
- so do I have to have an angle and angle side
- And it can't just be any angle angled side
- It has to be 40, 60 and 7
- And it has to be in the same order
- It can't be 60 and then 40 and then 7
- The if the 40 degrees side has
- if one of its side has a length 7,
- then that is not the same thing here
- Here the 60 degrees side has length 7
- So let's see if any of these other triangles
- have this kind of 40, 60 degrees
- and then the 7 right over here
- So this has the 40 degrees and the 60 degrees
- but the 7 is in between them
- So this looks like it might be congruent to some other triangle
- Maybe closer to something like angle-side-angle
- 'cause they have an angle-side-angle
- So it wouldn't be that one
- This one looks interesting
- This is also angle side angle,
- so maybe, these are congruent but we'll check back on that
- We're still focused on this one right over here
- And this one we have a 60 degrees, then a 40 degrees, and a 7
- This is tempting
- We have an angle, an angle and a side,
- but the angles are in a different order
- Here it's 40-60-7
- Here it's 60-40-7
- So that's an angle and angle and side,
- but the side is not on the 40 degree on the 60 degree angle
- It's on the 40 degree angle over here
- So this doesn't look right either
- Here we have 40 degrees, 60 degrees, and then 7
- So this is looking pretty good
- We have this side right over here
- Is congruent to this side right over here
- Then you have your,
- you have your 60 degree angle right over here
- 60 degree angle over here
- So it may not be obvious 'cause it's flipped
- and they've they're drawn a little bit different
- We should never assume that
- just the drawing tells you what's going on
- And then finally, you have your 40 degree angle here
- which is your 40 degree angle here
- So we can say we can write down that
- And I'll do it
- Let me think of a good place to do it
- I'll write it right over here
- We can write down that triangle ABC is congruent to triangle
- And now we have to be very careful with how we name this
- We have to make sure that we have the corresponding
- the corresponding vertices mapped up together
- So for example, we started this triangle at vertex A,
- so point A right over here that's where we have the 60 degree angle
- That's the vertex of the 60 degree angle
- So the vertex of the 60 degree angle over here is point N
- So I'm gonna go to N
- And then we work from A to B
- B was the side was the vertex that
- we did not have any angle for
- And we could figure it out
- if these 2 guys add up to a hundred,
- and this is going to be the A degree angle
- So over here, the A degree angle is going to be M,
- the one that we don't have any label for
- It's kind of the other side
- It's the thing that shares the 7, the 7 length side right over here
- So then we wanna go to N then M,
- and then finish up sorry
- And M, and M, and then finish up the triangle
- And oh!
- And I wanna really stress this
- That we have to make sure we get the order of this right,
- 'cause then we're kind of referring to
- We're not showing the corresponding vertices in each triangle
- Now we see vertex A or point A maps to point N
- on this congruent triangle
- Vertex B maps to point M
- And so you can say,
- "Look AB the length of AB is congruent to NM "
- So it all matches up
- And we can say that these 2 are
- congruent by angle, angle side, by AAS
- So we did this one is this one right over here is
- congruent to this one right over there
- And now let's look at these 2 characters
- So here we have an angle, 40 degrees,
- a side in between and then another angle
- So it looks like ASA is going to be involved
- We look at this one right over here
- We have a 40 degrees, 40 degrees, 7 and then 60
- And you might say,
- "Wait, here the 40 degrees is on the bottom
- and here it's on the top "
- But remember, things can be congruent if you can flip them
- If you can flip them, rotate them, shift them, whatever
- So if you flip this guy over, you will get this one over here
- And that would not have happened if
- you had flipped this one to get this one over here
- So you see these 2 by you have
- Let me just make it clear
- You have this 60 degree angle
- Is congruent to this 60 degree angle
- You have this side of length 7
- Is congruent to this side of length 7
- And then you have the 40 degree angle
- Is congruent to this 40 degree angle
- So once again, these 2 characters are congruent to each other
- And we can write
- I'll write it where I have to
- I'll write it right over here
- We can say triangle DEF, triangle DEF is congruent to triangle
- And here we have to be careful again
- D point D is the vertex for the 60 degrees side
- So I'm gonna start it at H
- which is the vertex of the 60 degrees side over here,
- is congruent to triangle H
- And then we went from D to E
- E is the vertex on the 40 degrees side
- Kind of the other vertex that shares
- the 7 length segment right over here
- So we wanna go from H to G
- HGI
- And we know that from angle-side-angle by,
- by angle-side-angle
- And so that gives us it
- That character right over there is
- congruent to this character right over here
- And then finally we're left with this pool chap
- And it looks like it is not congruent to any of them
- It is tempting to try to match it up to this one,
- especially 'cause the angles here are on the bottom,
- and you have the 7 side over here
- Angles here on the bottom and the 7 side over here,
- but it doesn't match up
- because the order of the angles aren't the same
- You don't have the same corresponding angles
- If you try to do this little exercise,
- when you map everything to each other,
- you wouldn't be able to do it right over here
- And this over here, you know,
- it might have been a trick question
- or maybe if you did the math,
- and this was like a 40 or a 60 degree angle,
- maybe then maybe, you could have match this
- to some of the other triangles
- And maybe some of them to each other,
- but this last angle and all of these cases,
- 40 plus 60 is a hundred
- This is going to be an 80 degree angle right over there
- They have to add up to an 180
- This is an 80 degree angle
- This is an 80 degree angle
- If this ended up by the math being a 40
- or a 60 degree angle,
- then it could have been a little bit more interesting
- There might have been other congruent pairs
- But this is an 80 degree angle in every case
- The other angle is 80 degrees
- So this is just alone, unfortunately for him
- He is not able to find a congruent companion
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
|
Have something that's not a question about this content? |
This discussion area is not meant for answering homework questions.
Discuss the site
For general discussions about Khan Academy, visit our Reddit discussion page.
Flag inappropriate posts
Here are posts to avoid making. If you do encounter them, flag them for attention from our Guardians.
abuse
- disrespectful or offensive
- an advertisement
not helpful
- low quality
- not about the video topic
- soliciting votes or seeking badges
- a homework question
- a duplicate answer
- repeatedly making the same post
wrong category
- a tip or feedback in Questions
- a question in Tips & Feedback
- an answer that should be its own question
about the site
Share a tip
Suggest a fix
Have something that's not a tip or feedback about this content?
This discussion area is not meant for answering homework questions.