I've cried three times in the past hour attempting to figure this out. I am currently in an online geometry course that compresses a whoel years worth of geometry into eight weeks. The videos my teacher provided were terrible audio quality, constant colour confusion, and overall just sloppy explanations. This video has put my mind at rest for the first time in hours. Your clear use of colours, the way you stepped back and explained reasoning + alternative reasoning behind every step, and offered lots of brilliant tricks to help remember something. You explained everything so well, and I am just so thankful that students like me have access to AMAZING teacher like you!!
@@stevenmontoya3054 the suck because of teachers like You if you were a good teacher they will understand you might be nice, but u don't know how to teach
Thank you so much I have looked at many guides seen many different way to do proofs and I’ve never understood them more than the way you explained it so a thank you from florida
Wow! You are so awesome Ms. Milkosky. I wish you were my Geometry Professor. I love how you calmly explain it, and you are not annoyed to do several examples. You are easy to follow. Your students are blessed by having you as their professor. I would like to understand two things. 1. When is HL used and 2. How do I do Indirect Proofs. I thought that it was a two column proof too, but not sure. I am taking Geometry this Fall, and I am determined to Ace the class with at least a B.
Thank you Kristy! Here are the answers to your questions: 1. You can only use HL when you have a right triangle. So if you have a right triangle and you know the hypotenuse of Triangle ABC is congruent to the hypotenuse of Triangle DEF and that Leg AB is congruent to Leg DE, then you can prove the triangles congruent by HL. 2. Indirect Proofs are sometimes called proofs by contradiction. What you do in this case is that you assume the opposite of the statement is true and then you try to prove that. Eventually you get to a statement that will contradict that assumption you made. At that point you are done!
Thank you!! I think that at this moment I can understand more how to do a proof... I was and I'm still have problems with proofs because I don't have any idea how to do it but I have an idea now!! Thank you... the video was clear and as you spoke was clear and understandable!! I think if I can do better with my next test!!
Hello Ms. Milkosky. Thank you for the amazing video. I'm an adult learner building up my math skills from the ground up, using (among others) TH-cam videos such as these. I've paused the video and found what I think is a different way of proving that segment LN is congruent to segment MN. Then as I watched the video and saw that you did it another way, I've paused before you revealed the next step and to my satisfaction saw that I did it the same way in my second attempt as you did. I'd like to know if my first attempt is also correct. Can you please take a look? Segments JM and KL intersect at point O. Angle KOM is congruent to angle JOL because they are vertical angles. Triangles KOM and JOM are congruent because of ASA congruency. Segments OM and OL are congruent because triangles KOM and JOM are congruent, and segments OM and OL are each other's corresponding parts (CPCTC). We can draw a line that connects point L with point M, because we can always draw a line between two points. Point LM is congruent with itself due to the reflexive property. Triangle OLM is isosceles, because both of its legs are congruent. Angles OLM and OML are congruent, because both of them are opposite to the two congruent legs of the isosceles triangle OLM. Angle JLO is congruent with angle KMO because of CPCTC. Angle JLO + angle OLM + angle OLN = 180 because they are supplementary angles. Angle KMO + angle OML + angle OMN = 180 because they are supplementary angles. The 2 equations above are both equal to 180, which means they are equal to each other. We can rewrite the 2 equations this way because of the reflexive property: angle JLO + angle OLM + angle OLN = angle KMO + angle OML + angle OMN Because angle OLM is congruent with angle OML, we can rewrite the above the following way: angle JLO + angle OLM + angle OLN = angle KMO + angle OLM + angle OMN Because angle JLO is congruent with angle KMO, we can rewrite the above the following way: angle JLO + angle OLM + angle OLN = angle JLO + angle OLM + angle OMN Angle JLO and angle OLM are on both sides of the equation, so they cancel each other. We get: angle OLN = angle OMN Since angle OLN and angle OMN are congruent, the sides opposite to them are also congruent, because of the property of isosceles triangles. The opposite side of angle OLN is segment MN. The opposite side of angle OMN is segment LN. This proves our statement that LN is congruent to MN. Thank you for reading my very long comment. It would make my day if you'd respond if this is a correct line of thought. Greetings from Hungary. Attila
The main problem I have with proofs is knowing which proof reason to use. From what I've seen, there are many different reasons and it's hard to just memorize all of it. I also have trouble finding where to start after the Given? Can't proofs be done in many different ways? Spotting the statements is very hard for me. Keep in mind, I don't have an actual teacher and I am trying to skip Geometry to reach Algebra 2 in the 9th grade.
Great question! Proofs can absolutely be done in many different ways, but you always start with the givens. In the proof videos, I talk about how your givens can lead you places and if you get stuck, look for things like shared sides, shared angles, and vertical angles. It's also true that certain reasons, like CPCTC, will usually follow the step where you proved the triangles congruent. Check out the links to the other two videos if you haven't already. There are more tips in them.
+Hana Malik Good question! In order the prove JNM and KNL are congruent triangles, you need to state that angle N is congruent to itself. I totally understand you're probably thinking "Obviously the two angle Ns are congruent, it's the same angle, why do I have to write it?" My students say the same thing. Proofs require that you write out every step, even the "common sense" ones. So if you state that triangle JNM is congruent to triangle KNL, you need to have somewhere that angle N in triangle JNM is congruent to angle N in triangle KNL. Hope this helps!
Sometimes it does, sometimes it doesn't. In this particular proof, you must do it in this order as each statement leads to the next. For example, you can't have reflexive property come after AAS because you need to prove that angle is congruent to itself before you can use AAS. The same goes for CPCTC. In order to use CPCTC, you need to prove the triangles congruent.
Great question! You can, you just have to make the drawing (figure) yourself. For a proof like this, you would need the figure given to you. I will try to do one where you have to draw the figure yourself and then I'll post the link here!
Some can be, but there is no general rule for how many steps it will take to solve a proof. Some could take 3 steps, some could take 20. The best way is to focus on what you are trying to prove, and let the steps fall into place.
The side that is congruent is not the "included side". Which, by definition, is the side directly in between the two angles. However if you prefer ASA, you could use the Third angles theorem to prove the last angles congruent and use either AAS or ASA.
u explained this 10000 times better than my teacher THNK UUUUUUU
because of this video i got 25.3/23 and i have no idea how that is possible but some how i got extra credit SO THANK YOU
SAME
simp
this was so long ago lol. still grateful XD
@@triggeredweeb111 someone likes mikey lol
I was to the point of tears trying to figure this out on my own, this video is a life saver. Thank you so much.
holy shit you cry over math
@@rat-ip4gr what a bitch amirite
Math is ass that’s why
Fr
you are literally still saving lives today. I actually understand proofs now, and they don't feel so daunting. Thank you!
I've cried three times in the past hour attempting to figure this out. I am currently in an online geometry course that compresses a whoel years worth of geometry into eight weeks. The videos my teacher provided were terrible audio quality, constant colour confusion, and overall just sloppy explanations. This video has put my mind at rest for the first time in hours. Your clear use of colours, the way you stepped back and explained reasoning + alternative reasoning behind every step, and offered lots of brilliant tricks to help remember something. You explained everything so well, and I am just so thankful that students like me have access to AMAZING teacher like you!!
i loved math until the alphabet got involved
Sameeeee
It’s better with the alphabet
Dante Bertin ya ur right. ^^
ive loved until they introduced proofs
Where are you live
no, proofs aren't fun in geometry especially when you have no idea how to use a two column proof but im learning :
Darn. My teacher doesn't teach "AAS" or "CPCTC" She teaches like Def of Segment Addition Postulate and stuff like that. :/
King Kirby oh , are you a 7th grader
Same
Not there yet
me too ugh
How fucked can your teacher be oml.
I'm glad there's people that I can learn from on TH-cam because my geometry teacher sucks.
I'm glad there's students who want to learn because my students suck
Steven Montoya lol
@@stevenmontoya3054 the suck because of teachers like You
if you were a good teacher they will understand
you might be nice, but u don't know how to teach
@@maryanne5280 Not all teachers are... bad so... How is Steven a bad teacher? Do you know them?
@@nobodyinparticular1116 saying"my students suck" is more than an evidence ha is a bad teacher.
Thank you so much I have looked at many guides seen many different way to do proofs and I’ve never understood them more than the way you explained it so a thank you from florida
You are a better teacher than my math teacher my teacher gave us one lesson on proofs and told us to figure out the rest
Thank you very much! A different teacher always helps!
Wow! You are so awesome Ms. Milkosky. I wish you were my Geometry Professor. I love how you calmly explain it, and you are not annoyed to do several examples. You are easy to follow. Your students are blessed by having you as their professor.
I would like to understand two things.
1. When is HL used and 2. How do I do Indirect Proofs. I thought that it was a two column proof too, but not sure. I am taking Geometry this Fall, and I am determined to Ace the class with at least a B.
Thank you Kristy! Here are the answers to your questions:
1. You can only use HL when you have a right triangle. So if you have a right triangle and you know the hypotenuse of Triangle ABC is congruent to the hypotenuse of Triangle DEF and that Leg AB is congruent to Leg DE, then you can prove the triangles congruent by HL.
2. Indirect Proofs are sometimes called proofs by contradiction. What you do in this case is that you assume the opposite of the statement is true and then you try to prove that. Eventually you get to a statement that will contradict that assumption you made. At that point you are done!
7:47 no
LMAO
lmao im daedddddddd bruh
Corresponding parts of congruent triangles are congruent= CPCTC!!!!
No, proofs aren't fun, but thanks for the help. I'll need it.
i wish i could give this woman a hug
Thank you!! I think that at this moment I can understand more how to do a proof... I was and I'm still have problems with proofs because I don't have any idea how to do it but I have an idea now!! Thank you... the video was clear and as you spoke was clear and understandable!! I think if I can do better with my next test!!
thank you soo much without u i wouldn't have finished my hw
I have my geometry final tomorrow and this just made me understand this topic sooo much more than my teacher teaching it in a trimester 😂😂😂
7:47 for you yes for students nightmare
Hello Ms. Milkosky.
Thank you for the amazing video. I'm an adult learner building up my math skills from the ground up, using (among others) TH-cam videos such as these. I've paused the video and found what I think is a different way of proving that segment LN is congruent to segment MN. Then as I watched the video and saw that you did it another way, I've paused before you revealed the next step and to my satisfaction saw that I did it the same way in my second attempt as you did. I'd like to know if my first attempt is also correct. Can you please take a look?
Segments JM and KL intersect at point O.
Angle KOM is congruent to angle JOL because they are vertical angles.
Triangles KOM and JOM are congruent because of ASA congruency.
Segments OM and OL are congruent because triangles KOM and JOM are congruent, and segments OM and OL are each other's corresponding parts (CPCTC).
We can draw a line that connects point L with point M, because we can always draw a line between two points.
Point LM is congruent with itself due to the reflexive property.
Triangle OLM is isosceles, because both of its legs are congruent.
Angles OLM and OML are congruent, because both of them are opposite to the two congruent legs of the isosceles triangle OLM.
Angle JLO is congruent with angle KMO because of CPCTC.
Angle JLO + angle OLM + angle OLN = 180 because they are supplementary angles.
Angle KMO + angle OML + angle OMN = 180 because they are supplementary angles.
The 2 equations above are both equal to 180, which means they are equal to each other.
We can rewrite the 2 equations this way because of the reflexive property:
angle JLO + angle OLM + angle OLN = angle KMO + angle OML + angle OMN
Because angle OLM is congruent with angle OML, we can rewrite the above the following way:
angle JLO + angle OLM + angle OLN = angle KMO + angle OLM + angle OMN
Because angle JLO is congruent with angle KMO, we can rewrite the above the following way:
angle JLO + angle OLM + angle OLN = angle JLO + angle OLM + angle OMN
Angle JLO and angle OLM are on both sides of the equation, so they cancel each other. We get:
angle OLN = angle OMN
Since angle OLN and angle OMN are congruent, the sides opposite to them are also congruent, because of the property of isosceles triangles.
The opposite side of angle OLN is segment MN.
The opposite side of angle OMN is segment LN.
This proves our statement that LN is congruent to MN.
Thank you for reading my very long comment. It would make my day if you'd respond if this is a correct line of thought.
Greetings from Hungary.
Attila
Love you mam..... You explained it very quickly.
OMG thank you so much! This was extremely helpful
way better at teaching than my geometry teacher
I didn't understand.
You teach better then my teacher my teacher just boring and just talks and talks and never stops
Your really good, keep up the good work!!!!
Can u be my teacher! I understand a little more now thx to u! Thank you soooo much!
I got a test on this next period and this helped me lol thx
good luck
@@gabriel-jh9qj i failed that class💀💀💀
@@faewisp LMAOOO
The main problem I have with proofs is knowing which proof reason to use. From what I've seen, there are many different reasons and it's hard to just memorize all of it. I also have trouble finding where to start after the Given? Can't proofs be done in many different ways? Spotting the statements is very hard for me. Keep in mind, I don't have an actual teacher and I am trying to skip Geometry to reach Algebra 2 in the 9th grade.
Great question! Proofs can absolutely be done in many different ways, but you always start with the givens. In the proof videos, I talk about how your givens can lead you places and if you get stuck, look for things like shared sides, shared angles, and vertical angles. It's also true that certain reasons, like CPCTC, will usually follow the step where you proved the triangles congruent. Check out the links to the other two videos if you haven't already. There are more tips in them.
Ms. Milkosky Thank you so much, I will keep that in mind!
and what is a CPCTC
Your voice is like music
Thanks, this really helped
OMG thank you ms. 🤗🤗🤗
youre welcome
this helped so much!
This was actually helpful
Why would you set the angle n's congruent to eachother?
+Hana Malik Good question! In order the prove JNM and KNL are congruent triangles, you need to state that angle N is congruent to itself. I totally understand you're probably thinking "Obviously the two angle Ns are congruent, it's the same angle, why do I have to write it?" My students say the same thing. Proofs require that you write out every step, even the "common sense" ones. So if you state that triangle JNM is congruent to triangle KNL, you need to have somewhere that angle N in triangle JNM is congruent to angle N in triangle KNL.
Hope this helps!
ok. thanks.
To prove JNM and KNL are congruent angles you need to state that angle N is congruent to itself
does the order of statements or reasons matter for proofs?
Sometimes it does, sometimes it doesn't. In this particular proof, you must do it in this order as each statement leads to the next. For example, you can't have reflexive property come after AAS because you need to prove that angle is congruent to itself before you can use AAS. The same goes for CPCTC. In order to use CPCTC, you need to prove the triangles congruent.
In some it matters, like this one so you can get the right answer since you can’t use reflexcive property come afte AAS
were now in proving triangles tho its a bit hard tbh😪😪
Very nice video
Tbh this lesson is the hardest ever for me so far
are you in 8th grade?
Well, I am and I am studying this so stop bullying this guy cause that is not nice and u should feel ashamed so yeah. This was such a sick burn
I liked math until I realized that I have to do math
good tutorial
Thank you mama
I wish you were my geometry teacher
ik this was 8 years ago but thx soooo much
really helpful! thank you
Nyc 💖
What if Theres no illustration ??? can you still answer the statements??? :3
Great question! You can, you just have to make the drawing (figure) yourself. For a proof like this, you would need the figure given to you. I will try to do one where you have to draw the figure yourself and then I'll post the link here!
Do you have any social medias? :) so that i can ask questions about like that? Because i really have a problem in math???
I do not, but check out Khan Academy. They have lots of videos and maybe some interactive stuff.
Youd have to draw out the image to figure it out
thank you ur the best
Can all Proof's be solved by 4 steps?Please answer me :)
Some can be, but there is no general rule for how many steps it will take to solve a proof. Some could take 3 steps, some could take 20. The best way is to focus on what you are trying to prove, and let the steps fall into place.
thanks
There is no general rule as to how many it’ll take to solve a proof
Well, I used to teach my classmates of how algebra or geometrics are, but now... I think I’m now the one who asks questions.. :’>>
just not mentioned on the figure that they are congruent
Why can't it be ASA?
The side that is congruent is not the "included side". Which, by definition, is the side directly in between the two angles. However if you prefer ASA, you could use the Third angles theorem to prove the last angles congruent and use either AAS or ASA.
Hmmmmmm since i have read Euclid's Elements, instead of writting angle N = angle N why not say " But the angle N has proven to be common" ??
Still good video !
Ms. Milkosky remember me
Please tell me I’m not the only ACE student here checking out how to get along with Geometry PACEs!?
nice...
notice me senpai
thank yo u if it wasnt for u i would have failed my grade 8 exam
I keep on repeating steps in proofs and skipping them too.
THANK YOU
Thank you!!!
wish u were my teacher
Thanks
I am a Teacher of mathematics from India
AAAAAAAH Math FUCK It !!!!!!
thanks mama
I’m so fucking confused this is too hard for me
thx this helped
2018 anyone?
easy peezy :)
You're too much sweet
Helpful video. OK. I also think you are very beautiful and not just intelligent
Hoooooooot
noice
Hot for teacher
and thank you for the vid my math teacher is old blind deaf and can barely see
I’m gonna fail
I am already -_-
Geometry was good until proofs 😔
cute
She hot
thanks