Triangle Congruence Theorems, Two Column Proofs, SSS, SAS, ASA, AAS Postulates, Geometry Problems
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- เผยแพร่เมื่อ 6 ก.พ. 2025
- This geometry video tutorial provides a basic introduction into triangle congruence theorems. It explains how to prove if two triangles are congruent using the SSS, SAS, ASA, and AAS postulate using two column proofs. Here is a list of topics contained in the statements and reasons of the two column proofs: Definition of midpoints, reflexive property, congruent angles, perpendicular lines, right angles, vertical angles, supplements of congruent angles, angle bisectors, triangles in circles, overlapping triangles, addition property of equality, segment addition, definition of congruent segments, and segment trisectors. This video contains plenty of examples and practice problems.
2 Column Proofs of Congruent Segments:
• Two Column Proofs of C...
2 Column Proofs of Angles:
• Geometry, Two Column P...
Triangle Congruence - SSS, SAS, ASA:
• Triangle Congruence Th...
CPCTC - 2 Column Proofs With Triangles:
• CPCTC Geometry Proofs ...
Median of a Triangle Formula:
• Median of a Triangle F...
Altitude of a Triangle - Orthocenter:
• Altitude of a Triangle...
_____________________________________
Triangles, Medians, & Altitudes - Proofs:
• Two Column Proofs - Tr...
2 Column Proofs - Isosceles Triangles:
• Geometry Proofs - Isos...
Angle Side Theorem - 2 Column Proofs:
• Angle Side / Base-Angl...
Hypotenuse Leg Theorem - HL Postulate:
• Hypotenuse Leg Theorem...
Detour Proofs - Double Triangle Congruence:
• Detour Proofs - Double...
Missing Diagrams - 2 Column Proofs:
• Missing Diagrams With ...
_______________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections
Final Exams and Video Playlists: www.video-tutor.net/
Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
Tomorrow is my exam
U replied after 6 years
Btw thank u for this video
Meeeeee
you already know test day is tmr.
Edit: Guys and gals, I was a sophomore when I wrote this comment. I’m now in college and I still cannot do math for shit. I work a part time retail job and I have to have my phone calculator out to do anything with math. Thanks for blowing my comment up 😂
For real
The accuracy 👌 my semester final is tomorrow 😂😂
@@choncho1169 Me too lol
Yassssssssss! Relatable!
it rlly is lmao
I have a geometry test tomorrow and my teacher has been teaching this for 4 days. I didn't understand it at all, and I was so confused. I am now 10 minutes into this video and I understand it all. Thank you so much.
Same here, literally
same im gonna fail
samee
@@adl0508Hey did you fail?
same for me thank for understand to me for this video
I learned all this in an hour and couldnt learn it in 2 weeks with my Math Teacher, I wish you were my teacher
hope I find the same luck you did. I haven't watch the video yet.
@@MenkaureBurns lol
Shortcut!
SSS - all sides
SAS - the A is in the middle, so the angle is included between the sides
ASA - the S is in the middle, so the side is included between the angles
AAS - the S is on the side, so it is not included between the angles (because it is excluded on the side)
Hope this helps!
Lmao EZ
your a hero man
i only got AA, SSS, and SAS at my school
@@alecpeay7790 ye same
So it's only congruent if it symmetrical to its counterpart
I just love how everybody who comment on this wasn’t prepared for their test at all
Dude mine is in 9 hours 😭😭😭
True😂😂😂
When the test was 2 days ago and you've been procrastinating it 💀
This helped me alot
Mines in 15 minutes
3 days of my my teacher explaining this=nothing
3 minutes into this vid and I understand it.
Infected348 same bruh
Ahaha
Periodt.
Infected348 one month of teacher teaching it vs 15 minutes and I get it
@@krisybasan tru bro
I love how my teacher doesn’t even bother teaching this subject himself and tells my class to go on TH-cam. This is honestly better and I think my teacher knows it.
honestly thats smart of him, kids do better when they can work at their own pace and learn at their own pace. u can pause and rewatch youtube videos, you cant tell teachers to when theyre teaching an entire class
It would be great if my teachers did the same too and just help me when I have queries instead of rushing into completing the syllabus
Savage trach😂😂😂😂😂😂😂
He's lazy
Doesn't that ruin the entire point of being a teacher, like what are they paying him for?
To anyone intimidated by the length of the video, I watched the video all the way through, and it was ENTIRELY worth it. Genuinely starting to understand the topic!
Let’s be honest, how many people are watching this right before their test?
Yeah
Me
Yup
1 hour before final I didn’t study for over break 🤪🤪🤪
Why else would i come here in the first place!? 14 hours b4 test
0:55 SSS Postulate Example
2:09 ASA Postulate Example
3:29 SAS Postulate Example
4:30 AAS Postulate Example
5:25 Composite Triangle; SSS Postulate
7:01 Composite Triangle; ASA Postulate
7:47 Vertical Angles Theorem
8:45 Not congruent Triangles
9:55 AAS Postulate; Right triangle
11:10 SAS Postulate; opposite of the side angle
12:44 SSS Postulate
13:30 Two Column Proofs 1
15:18 Definition of a midpoint
16:02 Reflexive Property
16:29 SSS Postulate
17:55 Two Column Proofs 2
19:16 Given (should be always the first)
19:40 Given (perpendicular line)
20:00 Right angles; perpendicular lines form right angles
21:07 reflexive property
21:28 SAS Postulate
22:14 Two Column Proofs 3
23:28 Given
24:10 Vertical Angles
24:44 ASA Postulate
25:18 Two column Proof 4
Literal lifesaver
@@spurk1994 it's not complete tho 😅
this is the right time to question how math would even help in real life
@@isha9300 I have a midterm exam tomorrow about them
And this is the right time to question how math will help me in real life
@@spurk1994 omg tysmmm
Best 50 minutes of my life.
I'm back from school and the test was very easy thanks so much
This really helps cuz online classes are even worse than face to face. Anyone else here in 2020?
meee
Yep, I hv my mid terms next week and I'm lessons behind
Yes
2021
Totally with you
Damn I wish he was my teacher, ive learned more in 1 hr than ive learned in 3 months
Wrxxd Gaming relateable
Wrxxd Gaming same, ive been In school for 2 months
I can relate bro
You are right bro
Hi brotha
My geometry test is in 8 hours. I’m not ready. Hopefully this works. 👏
PlatinumZars same situation
PlatinumZars uu
mine is in 2 hours
PlatinumZars did you pass
Mines is tomorrow fml
I've been learning this particular subject for like 2-3 weeks now and haven't understood NOTHING, til this video. Thank you so freaking much.
I have to take a unit test tomorrow and i feel ready because of this video.
Btw, i did my test and got a 85% I missed only 3 question
@@issaxv nice
nice
It's 1 am and I have a geometry test tomorrow..? Today? Whatever.
jessica m haaha it’s 3am
Kayla Gallow at this point don’t even go to school
4 am bitches
How'd you do?
Jonathan Augustin 46 lmaoooo
Didn’t understand this the entire month my teacher spent on it, five minutes into the video and I’m going through my review packet fast as hell. You’re a life saver 😭
Fr hahaha
I have finals next week and I am going through this guy's videos so I can get a better understanding, anybody else dealing with the stress of finals coming up?
Literally feeling it now, shit's too much for me.
how’d it go
yeah
This is me, but they're tomorrow and my school never bothered preparing me for it.
my brain went off the rails after learning grade 8 so i an really confused
It's a different struggle to cry over a math problem
yes it have different taste ;-;
@@adachi4043 ahh im so sorry to hear that!! That sucks
BRUH IM BAWLING RN I hate maths
@@blahblah1693 duuddee maths sucks arse but you've got this, I believe in you!!
Bro, I have to do the proof stuff and shit, and I know nothing cuz I had to miss school for 2 weeks cuz I got covid, but the test is tomorrow. I'm literally fucked
0:19 SSS≅ Postulate Explanation
0:30 SAS≅ Postulate Explanation
(0:36 Clarification: "A" stands for a pair of congruent angles, one in each diagram, and "S" stands for a pair of congruent sides, one in each diagram)
0:38 ASA≅ Postulate Explanation
(0:40 Clarification: "it has to be in order" means "the pair of congruent sides must be included (physically) between the two pairs of congruent angles in the diagram")
0:42 AAS≅ Postulate Explanation
(0:49 Clarification: HL≅ Postulate (aka HLR≅, aka RHS≅) is not discussed but is often considered a viable 5th option. See his other video: th-cam.com/video/DKSTjS0n3mY/w-d-xo.html&t)
0:54 SSS≅ Postulate Example
2:09 ASA≅ Postulate Example
(3:08 Clarification: second triangle should have the Δ symbol)
3:29 SAS≅ Postulate Example
4:30 AAS≅ Postulate Example
(5:21 Clarification: second triangle should have the Δ symbol)
5:25 SSS≅ Postulate Example (with Reflexive Property)
6:37 Composite Triangles Strategy (redraw triangles separately)
7:01 ASA≅ Postulate Example (with Vertical Angles)
(8:34 Clarification: second triangle should have the Δ symbol)
8:45 Example of Triangles With Not Enough Information
(9:32 Mistake: Instead of stating that triangles ABC and DEF are not congruent, state that there is not enough given information to determine congruence because the given information does not support any of the postulates. Triangles ABC and DEF could be congruent with 3 pairs of congruent angles, but we have no way of knowing for certain based on the given information in the diagram.)
9:55 AAS≅ Postulate Example (with Reflexive Property)
11:10 SAS≅ Postulate Example (with Vertical Angles)
(12:04 Clarification: second triangle should have the Δ symbol)
12:44 SSS≅ Postulate Example (with Reflexive Property)
13:27 SSS≅ Two Column Proof Example (with Midpoint and Reflexive Property)
17:30 Recommended Strategy for Learning Proofs
17:54 SAS≅ Two Column Proof Example (with Perpendicular and Reflexive Property)
22:14 ASA≅ Two Column Proof Example (with Vertical Angles)
25:18 SAS≅ Two Column Proof Example (with Supplements)
29:41 AAS≅ Two Column Proof Example (with Angle Bisector and Reflexive Property)
33:34 SAS≅ Two Column Proof Example (with Midpoint and Vertical Angles)
38:00 SSS≅ Two Column Proof Example (with Segment Addition)
43:53 ASA≅ Two Column Proof Example (with Supplements and Segment Trisectors)
Thanks mr.walters
MR. Organic Chemistry Tutor, thank you for another long-extended video/lecture on the Triangle Congruence Theorems and Two Column Proofs in Plane/Solid Geometry. From reviewing Geometry, my understanding of the two columns proofs continues to improve with practice and deep understanding.
Bros still saving lives 🙌 THIS WAS SUPER EASY TO UNDERSTAND TYSMMM. Let's pray that I get a 90% on my test.
I have to admit, my husband watched you for hours and hours and I got tired of hearing your voice but now that I have discovered why he watches you and how good you are, I love your voice....
I took geometry 3 years ago and I only just discovered this channel. I wish I discovered this channel sooner bc GEOMETRY WAS FREAKING ANNOYING.
I understood it here far better than I did in school.
When I return from school learning nothing.I can always count on you.This channel helped me a lot!
Thank you so much for doing awesome job! My daughter got struggle on this topic and she said her teacher didn't teach well, but after my daughter watched this clip, she understood right away!!!! You're doing so great job!
atleast this teacher wont shout at me when I couldnt understand the lesson
our teacher dont shout at us, but they do give a big chunk of homework and expect us to take an exam by the following day.
@@CR35C3ND0 thats sad
@@CR35C3ND0 They’re just making sure you do what you need to
What country do you live in?
Gghhhhhhggg
Bro may god bless you, my teacher has taught me geometry for 3 months and me and my friends haven't understood anything, but you helped me in less than 30 minutes, thank you so much.
unfortunately my boyfriend’s teacher sucks, so i had to watch this whole video to understand this 10th grade geometry. i’m still a freshmen but it doesn’t hurt to start early! And to be honest, this was the best understanding i could ever get. it’s so easy to him now since i re-teach it to him. thanks for the video!
update: we broke up😃 i have a girlfriend now🙅🏽♀️
@SUZETTE CAMILO we are !
Are you still together now?
@@mizukiyamada2371 we're still going !!
Update me future people
now?
4 years later but still extremely helpful for students, thank you so much
Wow thank you so much I was so lost before and this helped more than my geometry teacher ever did
This channel is a diamond in the rough, thank you for the help.
Thanks for posting this. This was a million times easier to understand than my geometry book, and my geometry book didn't even explain it to me with a visual example, it just said some stuff, and expected me to understand it.
legit my teacher explained this for 3 days and i didn't get it but i understood it after only 5 minutes. Thank you !!
Aced my test bro. Thank you so much
Why is this guy better than my actual teacher? I legit understood all of this and before I watched this video I knew jack shit about sss,asa,etc.
i literally love this. me and my bf are both in the 8 grade and doing ap subjects, this made us understand more. i adore this teacher, we both enjoyed it since we were fighting over who was right in the answers when the teacher asked a question. 😭
we both have a test tomorrow, wish us luck‼️‼️
Grade 8 and have a bf tf
One of those few times ( or the only time) I actually went through a video about maths fully and understood most if not all the stuff. Thanks!
Got a test in 15 hours...This is such a refresher since I was out so much and didn't get to learn the lesson. Wish me luck...
Hi, I am a regents exam scorer, and this year I will be grading the Geometry Regents. I was watching this video to see how most kids are taught, and I see a couple of things wrong. 1st. Always state all your givens in one statement, or this year it will cause reductions. 2nd. Always put the full definition. When you were proving one of the problems at 24:37 you put vertical angles, when the correct statement is intersecting lines form congruent vertical angles. While you will not lose points, it is just good practice, and it prepares you for further steps, because proofs have more than 1 way, so lets say along the way you realize that there is an easier option, but you can't do it because you did not list the full definition.
micheal do u have a video to help
Do you?
*2nd,*
That’s cool and all but when will we ever use this in real life
Ok boomer
So I'm very very bad at math, and I, couldn't understand it when my teacher taught this, but in less than 20 minutes I could already understand it. And take note, I'm really bad at math and it takes me time before I could understand a lesson. So thank you for this wonderful video!❤
gotta geometry final tomorrow and i’m the only one who has to take it and idek what i’m doing😚✌🏻
r a e l y n e l a i n e BROOO FRRR
thanks man i’ve got a shit math teacher and have a breakdown everytime she talks you the only reason i’m alive
This man is a gift from god, im legit studying this a day before exam, i did not understand this while my teacher thought me .
Damn got a perfect score on my math test just by learning from this vid, thx man you're a life saver
♡´･ᴗ･`♡
got my test tmr last minute procrastination this helped a lot
I learned more from you than my math teacher. Thank you so much for making this video
Thank you X1000, I was on the verge of giving up until I decided to actually use the internet for once. Your videos are very informational and helpful.
I am 5 minutes into this video and I understand so much more than te 2 weeks of my teacher teaching this! Thank you!
9:38 Be careful, it does not necessarily mean that they are “not congruent”, it just means that with the information that you are given (aaa) that you can’t prove they’re congruent.
If only all teachers taught this way
Test in 5 minutes. Length of video 50 minutes 😅
kobe thegoat Rip.
Did you pass? 😂
2x speed
Buddy taught me more than my teacher could in 2 weeks
Y helped me so much watching this at 10, test tomorrow, Bro I learnt more in 50 mins than 10 days of him giving us random worksheets and not attempting to teach us on how to do the 4.4 proofs.
thank you for this video. I needed for my geometry class
@SUZETTE CAMILO Yes hahaha
Thx a lot man this really helped me prepare for my math test
Tnx man you help me I past my exam
I have a teacher that obviously has trouble teaching, I ask him all kinds of questions about how to understand what he's teaching but it's like he's just repeating himself lmao, I'm putting my trust in this video because i no longer wanna seem like a dumbass 😂
Explained it a million times better than any Khan academy video. Thank you person from 6 years ago
Test tmr that determines if I pass the class I’ll let yall know! Edit: I PASSED! YOU GUYS GOT THIS. Just make sure you understand all the definitions and how to identify them!
Did you pass the class??
@ YES I did!
Thank you, my teacher mostly just explains her thought process so this helped a lot
Have me a test on this in about a week. Hope I can pick up everything by then 👐👐👐 (awesome video, really helping so far)
I passed! Thanks for the video!
@@artdump6997 YAAAAY okie help me now:)
Your explanation is marvellous..lots of praise from India.
This will now be my new teacher. My Geometry teacher isn't good at explaining. Thank You!
this video actually came in clutch
Good thing that this video is allowed to be downloaded yay!
I just wanted to thank you. You cleared up my confusion by explaining clearly. Your explanations were simple but yet I learned a lot
omg, you're a LIFESAVER my teacher didnt teach this, and I have to do homework... Thank youuuuuuu
I have a geometry test tomorrow, this helped me a lot. Thank you so much.
ActionJackson 114 same bruh
Your voice is so soothing, no homo.
Lol
Great video, the step by step tutorial shows me exactly how to do it correctly and there are many questions i can do to master the topic. I appreciate the effort and time you put into making these videos to help us!
You explain WAY better than my geometry teacher. He just mumbles and I can't understand him at all. Thank you
Thank you. This is much clearer that listening to the whole quarter class.
Thank you so much for this video! made me understand it more :)
tmr is my math exam sooo I'm here 😙✌
8:46 - 9:53 This is a bit misleading, sadly.
The AAA postulate (aka the AA postulate) cannot be used to prove triangle congruency, only similarity. It is a valid postulate for that.
So if you have AAA/AA, you can't say the triangles are _not_ congruent, you can only say that you cannot _prove_ them to be congruent (or not) without further information about at least one of the sides.
test tmr on this and u saved me ! just learned more in 1hr than 1 month of learning this in school.
This guy is one of the best teachers out there like i really learned alot from this video
Thank you bro
got a final exam tomorrow pray for me
How did it go
yea how did it go bru
@@itsnotaneon8344 pretty good!
@@angelsh6741 amazing!
@@meme_boi4202 nice
THANK YOU VERY MUCH FOR THIS WONDERFUL VIDEO! I HOPE I PAST THE TEST TODAY :)
Me too I got one in an hour
taught me more in a hour than 5 months in class
Omg at first I was literally crying fr and I'm so happy that I actually started running around and jumping thank u all my stress has been relieved thaaaaannnnnkkkkk uuuu!
Easy way for remembering!
S is for side
A is for angle
Therefore
SSS - Side Side Side
SAS - Side Angle Side (Angle is in the middle)
ASA- Angle Side Angle (Side in in the middle)
AAS - Angle Angle Side (side is on the side)
You can literally see how it works by remembering s is for side, a is for angle and looking at the structure of the three letters.
Also I didn't watch the full 50 minutes of the video so I'm not sure if he mentioned this or not, but there is also another proof called RHS, standing for Right Angle, Hypotenuse and Side.
best teacher ever
I have a test tomorrow wish me good luck 😂
Ashton The Baller how’d it go?
Me too someone wish me good luck tomorrow 🤣
how’d it go
@@v12-r82 how’d it go
summer geometry test is in 2 hours yikEs hope i do good
youre the best thing that has ever happened to my life
Its mu finals exam and im binge watching this guys geometry videos, this dude is the light to my life fr may you be blessed
I'm literally so confused because what my teacher taught us deviates from this
Same
same
Thank you soo much!! This was a HUGE help! I really appreciate it. 😁
Some one in 2019?
Kevi Osas test tomorrow on this stuff
Sofia Saenz how’d it go
I have to study this for a retake
Kevi Osas yea gotta Geometry rest tommorow
2020, suckah
Thanks a LOT! My congruence for my chapter understanding quadrilaterals is TERRIBLE so REALLY APPRECIATE this playlist.
i need to stop simping over this man's voice...
What-
thank you for saving me from failing my test lol online school is not it
fr
@@kalkidangg update: i got a C 🤪🤪
@@noekya.1560 omg same i got a C to lmao
@@kalkidangg LMFAOOOO painn
@@kalkidangg i have another test on friday too 💀
The amount of views on this video shows how hard Triangle Congruence Theorem really is
thanks for this video it really helped :)
No problem.
I really surprised how such a lazy person like me just watching the video and taking notes with an actual interest, i really hope my teacher explained that simply and understandable so you can understand the whole lesson in less than an hour .
Its the way i asked many of my tutors and i understood none of them but this actually HELPED me.
Do you have problems like that in your test or exams?
I'm asking because here in Greece, problems are much more complicated and, frankly, don't make an sense.
It's like lvl.1. you have to start someware
yes, we do. What are your problems like, because there is a reason I have to watch TH-cam videos. Maybe that is just my teacher then. IDK
@@siddarththota4047, well in order to solve the problems we are given you need to know the theory of other chapters as well. At least I don't have to deal with them anymore..
@@aether-29 oh okay. most of my tests individualize the chapter to only the one subject that we were learning. I can see how those types of tests are harder, since you have to review more than one chapter to study. This makes me think I have it easy in America, so why am I failing... JK I'm passing in my dreams...
@@siddarththota4047, I think that if you're failing, your teacher is, at least partially, to blame.