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Geometry Proofs Explained! Triangle Congruence

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On this lesson, we will work through several triangle congruence Geometry Proofs Examples and you will learn how to complete two column proofs and triangle congruence proofs step by step!
For more MashUp Math content, visit www.mashupmath.com and join our free mailing list! :)
This lesson answers the questions: How can I prove that two triangles are congruent? How can I complete a geometry proof? How do I prove vertical angles are congruent? How do I use CPCTC? How can I study geometry proofs?
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Опубликовано:

21 авг 2024

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Комментарии : 1 тыс.

@MashupMath 4 года назад

Thank you for learning with me! If you found this video helpful, please give it a THUMBS UP & LEAVE A COMMENT and be sure to SUBSCRIBE to my channel (I could really use the support!). Subscribe Here: bit.ly/2yRUQS1 -Anthony :)

@captainskull1418 3 года назад

fuck this link

@Creadas 2 года назад

Istg😞

@ratscribbles3713 4 года назад

Ngl geometry proofs have me crying for the test tomorrow

@tirthpatel336 4 года назад

mini bidOOF U eat pid

@evelynbaran8478 4 года назад

haha getting ready for my final 🥺

@masonelliott7674 4 года назад

I have one tmmrw tooooo😅😅

@cry_stalll 4 года назад

lol were literally everywhere

@snailzh 4 года назад

Made me get a fucking 47 smh

@arielleelse6776 5 лет назад

proofs make me cry thanks for the help man

@OmegaSpaghetti 5 лет назад

lmao same

@b-clasher 8 месяцев назад

Proofs are what amplify my depression

@sydneyosmus3650 7 лет назад

I am a visual learner and my teacher only teaches with notes so this is extremely helpful! Thank you so much

@MashupMath 7 лет назад

Thanks for the comment, Sydney! I'm happy to help! I hope that you can give this video a thumbs up and subscribe to our channel! -Anthony :)

@Phantom_Kraken 6 лет назад

Sydney Osmus I hate those teachers A visual understanding works for all especially in GEOMETRY WHICH IS ALL VISUAL!

@jessicaciarelli9285 5 лет назад

SAME

@Los_HermanitosCruz 5 лет назад

Same!!!

@nox9262 5 лет назад

My teacher just tells us XD

@meowcheesemeow6951 3 года назад

I OFFICIALLY THINK THAT GEOMETRY PROOFS ARE THE MOST USELESS THING AND THE MOST ANNOYING THING IN THE WORLD Edit: its been like 2 months and why the heck does this have 38 likes also the test for geometry proofs i got a 45 on

@arjunm6927 3 года назад

yes i agree, we need to learn about taxes and the government system

@aricohen9112 3 года назад

@@arjunm6927 ikrrrrrr

@spagetd1526 3 года назад

you probably did better than i’ll do

@Crimbtw 3 года назад

@@arjunm6927 thats something you learn yourself

@meowcheesemeow6951 3 года назад

@@phjsher yes i failed but i didnt't fail the class because the other topics were not as hard

@espadoodle5126 5 лет назад

This dude taught me what my teacher couldn't teach for almost a month...IN ONLY 10 MINUTES!

@Surge641 10 месяцев назад

My teacher taught us proofs for 2 days and is giving us a quiz about it now, she going by so fast

@Contier7 9 месяцев назад

@@Surge641bro i know

@Contier7 9 месяцев назад

@@Surge641and somehow like everyone else but me understands it

@Surge641 9 месяцев назад

@@Contier7 me 2 bro

@sk24-m9j 8 месяцев назад

REALL

@M5Javi 4 года назад

I fear no geometry problem But that thing.... That thing scares me...

@bassamabdullah9820 4 года назад

Same😂😂😂

@z4blu3m1n 3 года назад

I always fail these types of questions 😂

@deadethic 3 года назад

i donmt fdukcing get iut

@Iwanttoblowmybrainsoutrn 2 года назад

Same, I hate it so much

@kayaanm9643 2 года назад

bro same ask me to solve for x i would get it but this is some bs

@asma24 5 лет назад

Tip: If you don't know when to use CPCTC, just remember that CPCTC always comes after angle postulates.

@xThanya 4 года назад

what are angle postulates

@palmtoptiger1405 4 года назад

What is this word ur saying

@xThanya 4 года назад

@@palmtoptiger1405 I got a C in math as my overall grade :/

@xThanya 3 года назад

@Luke Bremner too late for that I already failed geometry, algebra 2 is so much easier for me I have an A I just never understood geometry

@nas3487 3 года назад

@@xThanya I’m in geometry rn😭 I got a test and I don’t really understand the proofs

@NN-tw7sh 3 года назад

im gonna cry. proofs will be the death of my geometry grade.

@nujiarts 2 года назад

Same T.T

@jo6ah 4 года назад

Who else came cause they have a quiz tomorrow

@Purplebloxian 4 года назад

Midterm today

@jo6ah 4 года назад

Sans Gamer same

@bimidairo1562 4 года назад

Test Today ;-;

@_kitty71101 4 года назад

@CalebPL 3 года назад

Yep

@banishedcorpse 3 года назад

When in my life will I care about triangles being congruent to each other 😀👍

@tswiftmeowmeowkittyslayer487 3 года назад

never LMAOOA

@sarahlynnr 3 года назад

LITERALLY

@bombtasticplays 3 года назад

Construction worker: that triangular roof right there is congruent to the one across it Other worker: what the fuck does that mean Bob?

@sarahlynnr 3 года назад

@@bombtasticplays good thing im not gonna be a fucking construction worker

@regularguy9043 3 года назад

Asked my teacher this and she said, you will never use it, her class is fun

@sisterjimin-ahshalallifegu8211 5 лет назад

This hard I’m rippin my hair off tryna get this....Edit: I failed the test

@faizadaud4085 5 лет назад

BTS Army Rocks hahahah

@annmargaretcapispisan7590 5 лет назад

BTS Army Rocks mood

@lupita6446 5 лет назад

ARMY!

@sisterjimin-ahshalallifegu8211 5 лет назад

Grilled Fish and steak wasssuppp

@maxdvmoon8739 5 лет назад

Co-army!!! Huhuhu. Hopefully I won't fail later on my test. 😂😭

@verahaile8568 4 года назад

watching this right before my test trying to find something ANYTHING to help me pass... wish me luck

@heyhowareyou8165 3 года назад

been 10months how'd you do lol

@daniyalbasra4330 3 года назад

how did u do on the test?

@heyhowareyou8165 3 года назад

@@daniyalbasra4330 i think failed lmao

@daniyalbasra4330 3 года назад

@@heyhowareyou8165 dang man. keep your head up and study harder for the test unless ur asian like me and get beat up for bad grade yikes

@heyhowareyou8165 3 года назад

@@daniyalbasra4330 OOOF that used to be me but like not

@davidhope6450 4 месяца назад

13 years later and this finally helped me understand proofs. Thank you drunk curiosity

@peacelovedolls1672 6 лет назад

I know this is a bit of an old video, but it was super helpful! I've been having a super hard time with proofs in geometry. I always get stuck halfway through and have no idea where to go from there. Sometimes I'll skip a step because my brain simply finds it too logical and easy to even consider it as a step, I guess. This definitely gave me a better understanding! Thank you for the help! :P

@aidanrobleto9013 5 лет назад

I realize that this is a bit late, but I've found that working backwards can be really helpful--basically, you see what you need to do to prove the final statement, and then see what you need to do to prove that, etc...

@moisesfernandez4885 Год назад

@@aidanrobleto9013she already graduated😂

@Ok-jt1ml 8 месяцев назад

Deadass

@farkhasamak3098 3 года назад

UR LITERALLY A SAVIOR....my teachers been tryna teach this for the past two weeks and i have a test next wednesday and this helped SO MUCH thank youuuu i literally love u oh my god

@mikk4446 4 года назад

you just taught me what we spent 2 months learning in 10 minutes. ☺️

@__szn__ 11 месяцев назад

We only had like a few days to learn it before the test lol

@gaymf469 4 года назад

My test is in a few hours and im sobbing😗✌🏼

@daniyalbasra4330 3 года назад

@@fluff7212 how was it?

@fluff7212 3 года назад

@HALA MOHAMMED [Student]i don't wanna look at the grade cuz i'm scared 🙄

@fluff7212 3 года назад

@@daniyalbasra4330 it was terrifying i ended up accidentally missing two questions which prolly deducted my test grade :/

@daniyalbasra4330 3 года назад

@@fluff7212 dude same i got every question correct but i got this matching question that was worth like 30 points and i got like all of those wrong.

@fluff7212 3 года назад

@HALA MOHAMMED [Student] i watched this after the test bc i needed this for a hw assignment

@daniyalbasra4330 3 года назад

Who else here is taking Honors/Pre-AP Geometry in 9th grade?

@bobbob-nj3ck 3 года назад

!!!!!!!!!! dude me, honor geometry?? that doesn't exist does it??

@rishabpeddi3857 3 года назад

@@bobbob-nj3ck it does I’m taking it

@xxdayxx9289 3 года назад

8th grade for me and I’ll tell you... it’s TOO MUCH

@daniyalbasra4330 3 года назад

@@bobbob-nj3ck It does. Well in my school it does lol

@emmahagaman3613 3 года назад

and i’m struggling😂

@mr.r1178 3 года назад

Why do we even learn this, we're not even gonna use this when we grow up

@ivanmendoza2044 3 года назад

That’s why u shouldn’t stress too much on it. As you said, you are not gonna use.

@triplewavy9882 3 года назад

@@ivanmendoza2044 yeah but it's still gonna impact your grade if you dont learn it

@katherinegarnicasuarez 3 года назад

It helps us think analytically and introduces us to deductive reasoning. In other words, you won't be naive in real-life because you'll ask for evidences and proofs for given facts to test if it is true.

@triplewavy9882 3 года назад

@@katherinegarnicasuarez While that is true, I definitely feel as if there are other ways to learn how to think analytically that isn't doing PROOFS. It's annoying, boring and practically useless for most careers, and it just runs everyone's grades lol

@katherinegarnicasuarez 3 года назад

@@triplewavy9882 I understand your point. However, everybody's experience is different. I have found geometry proofs actually useful in my life for credibility (politics, science, and also computer programming). But I respect individuals who think otherwise.

@nico-ui9oi 5 лет назад

how do you predict what the next step is

@tidebleach1253 5 лет назад

That’s exactly what I was thinkin

@millyslime1190 5 лет назад

basically like he said you litterally have to use what you know

@millyslime1190 5 лет назад

its hard bro

@Celestials1aurora 5 лет назад

MillySLIME do you think you can help me?

@Celestials1aurora 5 лет назад

xKamanche did you ever find out if you did please let me know 😢😢😢🤕🤕🤧😭😭😭

@StickmanKobe 4 года назад

Bro I’m recommending your channel to my friend who has geometry next year, I’m in honors and your stuff helps so much, thanks man.

@MashupMath 4 года назад

Happy to help!

@Delta37815 8 месяцев назад

Bro I sat in class for months not understanding a single word my teacher was saying but this just made me understand literally everything in a few minutes. Thank you so much!

@brendenhandley9281 2 года назад

I haven't been able to understand proofs all year, and I have an exam tomorrow so thanks, man.

@RibbonSealTiff 4 года назад

You just taught me more in this video than I have learned in the past marking period of geometry

@yesvelin 3 года назад

geometry class is just me crying cause im confused

@angelumacob4597 3 года назад

SAMEE

@Swtred1965 7 лет назад

Awesome lesson; graphics were very beneficial. We'll be looking for more tutorials from you.

@MashupMath 7 лет назад

Thanks for the comment, Thelma! I'm so glad that you enjoyed the lesson and hope that you can subscribe to our channel and share it with others! -Anthony :)

@DanteWolfwood 2 года назад

You know, if they taught kids Discrete Mathematics BEFORE Geometry and Algebra, this would make a lot more sense to kids.

@samcabrera2316 2 года назад

Honestly, I didn't know what the heck Discrete Mathematics was before. After graduating from college, I realized that it should be taught to kids before any math subject like Algebra, Trigonometry, or Geometry.

@drew54948 3 года назад

In my opinion, proofs in geometry are idealized, perfectly sound arguments and are good for teaching logic like you would learn in a philosophy class. You likely won’t work with triangles in your career or in other problem-solving, but you will need solid reasoning skills for any meaningful decisions.

@arrianah5080 Год назад

this is also what i was thinking!

@InfinityGGG1 2 месяца назад

Ah yes, We need the skill of knowing that this or that is congruent for an important decision.

@Sprinkles7652 2 года назад

This was super helpful. My teacher always rushes through the lessons before I can even know what’s happening. She’s also never available to help with problems because she only comes in for two periods and then leaves. Thank you for being the math teacher I don’t really have 👍

@johnessig3870 7 лет назад

i kneel before u my math god

@Cr1zby 6 лет назад

john essig he's not a god

@angelumacob4597 3 года назад

@@Cr1zby true but it's a joke

@joshuafurtado1331 4 года назад

I'm a new teacher (even though I'm 41), and while I've taken courses in proof, this video helped me teach it to my high school students. I show the video with instructions, visual, and allowing them to follow along I get them all to at least grasp the concept. Thank you so much for this video and others I will use.

@nataleeisjustchilling2737 2 года назад

You're a whole lot better than my teacher, I nearly failed a proofs quiz because I didn't understand basically anything on it

@simonbalfe6140 6 лет назад

thanks so much, i find geometric proof very hard however this has strengthened my confidence greatly in this.

@pamelawisebronson3511 5 лет назад

Thanks so much for this - I'm going to have my students watch it. I think it will help them feel less afraid of having to do proofs.

@palmtoptiger1405 4 года назад

Pamela Bronson I thought u had to teach them??

@amberuidenich5477 5 лет назад

I think this will really help my students who need more help with proofs, thank you!

@shaquille.oatmeal672 9 месяцев назад

I have a geometry test coming up about proofs and I had no idea how to do proofs and now I do. Thank you for the vids helped me a lot.

@MontoyaMonsters Год назад

Bro you taught me more than my geometry teacher did in 2 months tysm

@theburger_king 9 месяцев назад

im still failing geometry

@normanfckingrockwell5544 8 месяцев назад

Honestly me too

@lordofcinder668 9 месяцев назад

I was stressing I over a test but now I have much more reassurance thanks

@Cinnamonhopeful 5 лет назад

I have a final in geometry tomorrow and proofs are it's concept but I understand this WAAAY more than my teacher! Thank you so much!!

@gentryburns8240 4 года назад

this is the most helpful thing i’ve ever watched

@marias5149 3 года назад

Thank you SO MUCH. Proofs have been killing me, and this video made me feel just a little bit better about them

@Zoe-fu7bt 5 месяцев назад

I was in honors’ geometry in high school and it was the hardest class I ever took. Proofs were definitely a challenge for me, but I worked hard and still got an A. I liked the puzzles!

@ariellenahh 5 месяцев назад

good job for getting an A! im in the middle of geometry this semester and i hate proofs sm

@scaramooch7103 Год назад

I still don't understand proofs even after watching this video 💀 and I have a test in an hour

@anticorncob6 Год назад

The word "proof" essentially means the same thing in math as it does in normal English.

@florencedupingayvedar5427 7 лет назад

thank you sir anthony for the very clear and articulate presentation of the lesson..i look forward to all your videos on math lessons,

@marchhare9039 2 месяца назад

I came here as a 25 year old to remember why I never understood proofs when I took geometry; I'm beginning to realize that it probably had something to do with the Christian faith I had. "Why do I need to prove something that I already believe is true?"

@Allizt 4 года назад

I just remembered i had an assignment and i need to do it now

@KarenLMcLaren 8 лет назад

First proof has a minor issue: the triangles should be named so the corresponding parts match up. You can prove that triangle GFK is congruent to triangle JFH by SAS.

@MashupMath 8 лет назад

+Karen McLaren Thanks!

@althor2388 2 года назад

POV your watching this in bathroom while every one is taking the test

@ajbeew2257 2 года назад

"I know they drive you crazy", crazy is an understatement.

@melinibethrivera3972 4 года назад

You are so good teaching! I’m a latín person, and I understand your video 🥰

@tarekhussein5326 3 года назад

I'm arab

@sophiaking2083 4 года назад

y’all if anyone can help i have a test tomorrow pray for me and i missed a week of school

@charlotte8927 4 года назад

Sophia King I felt this on a emotional level dude,, I missed the first two weeks of school so I missed a whole unit and a half of geometry so now I’m insanely behind and my teacher is barely helping me ;; plus I have to take two math tests tomorrow on stuff I’m not comfortable with yet aaaaaa;; but I hope you did well on your test 🥺

@girlover123 3 года назад

how’d U Do ?

@vibecheck8420 3 года назад

Did ya pass?

@paulspringer1873 7 лет назад

Clutch

@SyCoSaMiR 4 года назад

ur the teacher I need irl lmao

@derbyplayz8845 6 месяцев назад

2024 anyone 😭😭😭

@bradywelch196 3 года назад

Who’s here the day before the test

@justjenn5330 5 лет назад

My teacher doesn’t even take notes. He hands us a worksheet and expects us to know something I’ve never seen before.

@donnarenee71 Год назад

Now I understand! Thanks so much for this.

@mac2240 5 месяцев назад

geometry is so easy but with proofs there’s so many theorems and stuff to remember

@ariellenahh 5 месяцев назад

@mebeingme9881 3 года назад

I literally stopped paying attention in my zoom class 😔

@lol2094 7 лет назад

So helpful and easier to follow than the other tutorials on youtube. I subbed :D

@andreajasyl2655 2 года назад

this is the dumbest thing I’ve seen in geometry, sure I can give the statements, but the reasons? I feel like I’m making up definitions as I go.

@sophia5608 Год назад

Very helpful! Wish me luck for my exam tomorrow, but this really helped me thank you!

@lex4992 4 года назад

I’m not even in geometry yet I’m just watching bc my geometry friends keep warning me about these

@sportingdirector1 3 года назад

They were right to

@tortugaez9063 3 года назад

when a yt video explains it better then your teacher

@KokoYukii- 2 месяца назад

Thank you this helped since I have an exam tomorrow that will determine if I have to take the exam again in the next semester or if I get to carry on happily with my life, I’ll update my thoughts after the exam and what I ended up getting, mostly for myself to see if I actually lose it or not but right now I’ll be pretending to be hopeful ☺️🔫 Update 1: I am literally so cookeddd there’s no way I’m not taking that exam again 😭 Update 2: unlike the first update I got a 69% i literally scraped by, by the skin of my teeth but if I can pass so can you, I literally sucked at geometry 💪

@chia7909 5 лет назад

Thank you for this! I wasn’t able to understand some because of my teacher but this is really helpful. Thank you!

@kieran_stainton6771 5 лет назад

extremely helpful especially with the colours!!!

@jioonn 6 лет назад

so im having troble on which postulate goes with the result of a specific proof, my teacher tells me that any COULD work, as long as you prove it properly, but i cant find the correct postulate

@ymm424 4 года назад

Keep the 9th grade algebra and 10th grade geometry material coming PLEASE. Great stuff.

@swgtcca4327 3 года назад

i jus wanna give this dude a really good hug and thank him

@GhostBoyVideos 7 лет назад

Thanks! Helped a lot.

@MashupMath 7 лет назад

So glad to help! I hope that you can subscribe to our channel and share it with others! -Anthony :)

@alexandravermeulen2654 3 года назад

at this point i’m just accepting failure

@Emeryy_h 2 года назад

this is so helpful. more than my teacher has ever taught me. I am definitely subbing!

@Hecateofcrossroads 2 года назад

How do you know how many statements and reasons there are without a set up like that?

@surya_anand Год назад

anyone here in 2023??

@chinchilla57 5 лет назад

The visuals are solid. Thanks! I'm going to use this in the class I am subbing in

@chloeb7539 2 года назад

i have a quiz on this in an hour. i’ll update when i get my score!

@Gabi-pn1fw 2 года назад

How’d it go?

@kidleroy5424 3 года назад

teacher : are y'all following student : no teacher: great

@CaspianTheGh0st 3 года назад

“We always have a diagram” WHAT I DONT EVEN HAVE A DIAGRAM

@farkhasamak3098 3 года назад

Huh- proofs cant work without a diagram...ur teachers weird bruh

@vanessavlogs_xxl3739 3 года назад

When I haven’t payed attention this whole chapter so I’m watching this at 6:30 am to learn it b4 the test Update I got a d and I though I did good so literally gonna go die

@ethansantillan714 Год назад

you dont know how much this helped me

@iy36 Месяц назад

tysm, im preparing for my geo class in the fall and this helped me learn proofs early.

@laservoid2908 4 года назад

i have to do this *in a different language* imagine that

@kellymacias7340 11 месяцев назад

This is legit one of the stupidest math topics i'm ever had to sit through, doesn't help that my teacher is actually the worst at teaching

@C17YES 11 месяцев назад

@Surge641 10 месяцев назад

@itsvk6 2 года назад

Bro i kinda forgot about proofs cuz i was busy with all the other topics plus i have a CBE tommorow where i get to skip geometry if i pass the test and this video really helped alot man thank you

@yasmarirosa-kb2pd 5 месяцев назад

as someone who has been struggling thank you soo much this video was so helpful!!!

@KenyaMelvin 4 года назад

*me, sitting here trying to figure this out because school has been canceled and we have e-learning*

@yagirlmal8833 5 лет назад

THIS IS SO FRICKIN HELPFUL I HAD SO MUCH TROUBLE WITH THIS LESSON BUT THIS T H I S H E L P E D M E S O M U C H

@levioneill9677 2 года назад

Thank you so much! I couldn't explain this to my 2nd grader who is awesome at math, while I suck at math. I'll be back for more soon, I'm sure. Thank you!

@itzaira-me8057 7 лет назад

this was actually very helpful it's better than some online tutor you have to pay for. Thankyou so much

@reganbates8300 8 лет назад

this was helpful , thank you

@MashupMath 8 лет назад

+Regan Bates Awesome! So glad the lesson was helpful. If you have a sec, please subscribe to our channel and share it with your friends and classmates. We could really use the support! -Anthony :)

@xjustchillx9665 5 лет назад

Holy shit I’m freaking out. It’s my test tom and it’s 11:30 pm rn, I don’t wanna fail. Edit: omgomgomg I got the result today and it was 100! Thanks!

@gooeylifts 4 года назад

no one asked

@ezhq1 Год назад

After watching this video, I feel like my brain size expanded. This helped so much in allowing me to understand how to structure the proofs and organize my reasons in to logical arguments.

@terreciakennedy3265 3 года назад

That was a good explanation. Here learning math all over again to be able to help my 10th grader with geometry.

@dissapointment451 3 года назад

I failed a final for not knowing this so i decided to get my life toghether

@jadenpatron1959 6 лет назад

I was wondering whats a good website to learn all of my def. of ..... Bisect for example

@Sushigabby 6 лет назад

i dont know if this is what you're looking for but it may help? Sorry.. quizlet.com/6486216/geometry-postulates-theorems-properties-and-definitions-for-proofs-flash-cards/

@akshitha4643 5 лет назад

sushigabby123 Thank you!

@q9954 4 года назад

This is an excellent, clear video! However, in the first proof, it has not been proven that triangle GFK is congruent to triangle HFJ because segment GF is not necessarily congruent to segment HF, and segment FK is not necessarily congruent to segment FJ. Corresponding parts must be given in the same order. To make this proof correct, prove that triangle GFK is congruent to triangle JFH.

@matthewspallina226 6 месяцев назад

I was supposed to have a test on this in 11th grade but I was extremely lucky not to have it cause my teacher decided not to give one. That made me so relieved cause I struggled so much with proofs even when I was tutored.