Altitude to the Hypotenuse of a right triangle (Mean Proportional)

In this video I will introduce you to the three similar triangles created when you construct an Altitude to the hypotenuse of a right triangle. I will go through how we know those triangles are similar, and several examples of how you can use this fact to solve for various lengths given some information about the picture. To skip to the examples go to 5:23 You can download my notes in pdf form and follow along with the video if you like: drive.google.com/file/d/1b4IK...
NOTE: I know there are faster ways to solve these types of problems, I've even made videos about them years ago, but after teaching this topic for years, I've found that by relating it directly back to the three similar triangles students have more success in solving these problems (especially after some time has elapsed as this method requires no memorization beyond a simple understanding of similar triangles). If you'd like to watch the old video you can do that here: • Mean Proportional Righ...
#MeanProportional
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#GeometryHelp

[@nabi842]

finally a video that takes it time and actually explains it. thank u

[@OffRob_]

I typically never comment but I'm a sophomore in high school and i'm supposed to be taking a test on this. My teacher has tried to teach us time after time and no one understood. Here I am 10 minutes into the video and now I understand how to do this from start to finish. Thank you, much appreciated🙏

[@RealMikeDobbs]

Oh wow, that's such wonderful feedback, I'm so glad it helped you. Thanks so much for letting me know 😄

[@getrolled613]

you explained everything so clearly and step by step! THX!

[@RealMikeDobbs]

Thanks so much! Glad you found it helpful 😄

[@ericaknierim4663]

Thank you so much! You explained it so well. My son and I watched this and it really cleared up this concept for us.

[@RealMikeDobbs]

That's terrific! Thanks for letting me know 😄

[@welayinthorns747]

Thank you!! I'm in quarantine and my school doesn't have online classes so my geometry teacher just assigns us a bunch of work with no explanation of how to do it. This is the first video that really helped me grasp the concept.

[@RealMikeDobbs]

You're very welcome- thanks for letting me know! I have many more Geometry videos on the channel so be sure to look around. Also, I'll be adding an entire series on circles in high school Geometry over the next few weeks.

[@muskanmeena6963]

@@RealMikeDobbs thank u

[@RealMikeDobbs]

@@muskanmeena6963 You're welcome 😄

[@learWARA]

Wow, thanks alott, I've been trying ti find the right video for 3 hours straight. Thankss alottttt

[@RealMikeDobbs]

That’s terrific! Glad it helped you out, thanks for watching 😀

[@imxtr45h]

i finally understand it after 4 other vids ur the best u just earned a sub

[@RealMikeDobbs]

That’s great to hear Corey! I’m really glad it helped you out 😀

[@_csm]

I completely forgot how to do this stuff. Thanks a lot👍

[@RealMikeDobbs]

You’re very welcome 😀

[@justmyopinion7233]

4 years old and it's still helping students, tysm for this, it is really informative and understandable

[@RealMikeDobbs]

Thank you so much 😀 It’s always wonderful to hear from people who find my videos helpful.

[@Samisai]

amazing explanation, will help on my quiz tomorrow!

[@RealMikeDobbs]

Thanks so much! Very glad to know it helped you 😀

[@LienLe1]

Super clear and easy to understand. Thanks.

[@RealMikeDobbs]

Glad it was helpful!

[@sachindeshpande8923]

Nice explanation, thanks

[@elhaselkim11]

Great Job! I'm a student teacher and I'm suppose to teach this topic You're explanation is what my students need! Thank you for sharing!

[@RealMikeDobbs]

Thanks so much, I'm glad you found it useful : )

[@paulm9523]

Student okay STUDENT TEACHER BRUH U NEED GEOMETRY IN UR LIFE

[@diegomora3202]

Thank you SOOOO MUCH u made it so easy for me to understand

[@RealMikeDobbs]

That’s awesome- thanks so much for letting me know 😀

[@matheds5043]

Thanks a lot. Amazing explanation.

[@RealMikeDobbs]

Thank you so much! Glad you found it useful 😀

[@Jeran-vy1nb]

My good sir I thank you , my zooms aren’t enough teaching and this helped simplify things alot

[@RealMikeDobbs]

That's great to hear, thanks so much! 😄

[@aknurnursalbek7205]

It was a really helpful video, thank you so much!!!!!!!

[@RealMikeDobbs]

That great to hear, thank you 😄

[@Shai259]

Really helpful and understandable!! I watched many videos on this and this is the first one I understood

[@RealMikeDobbs]

So glad you found it helpful : ) Thanks for letting me know.

[@Numbers-n-Innovations]

@@RealMikeDobbs same here, i watched two three videos, but was still confused. This was really helpful

[@omkumar251]

coól i mean its so clear and easy to understand great work dudë

[@RealMikeDobbs]

Thanks so much! I'm glad you found it helpful 😄

[@3t3rnalap3x5]

Great video sir! You really helped me learn this topic for math

[@RealMikeDobbs]

Thank you so much! Glad to hear it helped 😄

[@dawsontate2989]

This video was great!!

[@RealMikeDobbs]

Thanks so much! Glad you enjoyed it 😄

[@math-cafe]

I love your work what is the program you used ?

[@RealMikeDobbs]

Thanks! I am using smart notebook for the workspace (which unfortunately is kind of pricy), and Screencast-O-matic to record the screen (awesome free tool).

[@sidramuntaha8230]

Awesome videos. I wish my son got a teacher like you.

[@RealMikeDobbs]

Thank you so much ❤️

[@slick8403]

thanks this really helped me understand this topic better

[@RealMikeDobbs]

So glad to hear that 😀

[@nehalrevuri8003]

Wow this really helped me thank you so much

[@RealMikeDobbs]

I'm so glad, thanks for letting me know 😄

[@anurudhawasthi4241]

Sir yours maths videos are very helpful Thank you

[@RealMikeDobbs]

You're very welcome : )

[@alozin5339]

Thank you so much this helped a lot

[@RealMikeDobbs]

That's terrific, so glad it helped you 😄

[@getrolled613]

thx so much

[@marly1719.]

You are awesome!!!!

[@RealMikeDobbs]

Thanks so much- what an awesome comment 😄

[@hazimalkurishy9100]

all three sides of triangle are initially meters in length , one of the triangles sides is oriented horizontally the triangle is scaled down in size without changing any angles , what is the new height of triangle when area is exactly half of the original triangle area ?

[@RealMikeDobbs]

I'm not 100% sure of the question your'e asking, but here's my best shot. If the area of the triangle AFTER the dilation ends up being 1/2 the original area, then the triangle must have been dilated by a scale factor of 1/(sqrt(2)), or rad(2)/2. Therefore, ALL lengths of the new triangle will be that scale factor times the corresponding length in the original triangle. If the original triangle had a height of H, then the new triangle has a height of Hrad(2)/2. Does that answer your question? If not, let me know. If you're interested in learning more about similar triangles in general, check out this video: kzbin.info/www/bejne/ipiomYycoLGAetk

[@djamesgraham]

fantastic job!

[@RealMikeDobbs]

Thanks very much Jim! I'm working hard to put out 3-4 new Geometry and Pre-Calculus videos a week right now. If you know anyone who may benefit from them please share the channel 😀

[@bastibagirova2002]

Which tool do you use to write expressions?

[@RealMikeDobbs]

I work in Smart Notebook for the slides and handwriting. The typed equations are made with MathType and screen captured into Smart Notebook.

[@osmantabet7104]

Thank you soooo much

[@RealMikeDobbs]

You’re very welcome 😀

[@nashidac501]

Thanks for this class

[@RealMikeDobbs]

Glad it helped 😄

[@lynlao2927]

How do u find the altitude when ur given 20 instead of 18 and 2 for the base??

[@RealMikeDobbs]

You’ll need to be a little more specific there, I’m not sure what you’re asking.

[@Regular_Decorated_Emergency]

Thanks. 🙏

[@RealMikeDobbs]

You’re very welcome 😀

[@elclinify9922]

Thank you...

[@RealMikeDobbs]

You’re very welcome- glad to know it helped 😀

[@vinniechhabra6257]

Thanks! This is helping me help my son with his 10th great geometry homework

[@RealMikeDobbs]

I'm so glad you both found it helpful!

[@human6211]

Nice one 🙏

[@RealMikeDobbs]

Thank you 😀

[@undercover9647]

My last proportion looks a little different from yours. I wrote 6/x=x/54. Does that matter?

[@RealMikeDobbs]

You're good. As long as you set up a valid proportion you will get the same equation when you "cross multiply." Notice that when you "cross multiply" you get 5(54) = x^2, same as me. 👍

[@undercover9647]

@@RealMikeDobbs How do I know that I set up the proportion correctly?

[@RealMikeDobbs]

Well, I guess I don't truly know. You could have done something wrong, that happened to end up with the right proportion, but I can tell you that your proportion is A valid proportion for this problem. Here's ONE way to arrive at the proportion you have. Starting with 6 in the smaller triangle. 6 is between the right angle and the one tic blue. In the larger triangle, between the right angle and one tic blue you find x. Then, back to the smaller triangle, the hypotenuse is x, which corresponds to the hypotenuse of the larger triangle, 54.

[@mdjahidulislam9205]

saved my day

[@RealMikeDobbs]

God to hear it- lots more videos on the channel. 👍

[@honest_bibliophile]

Also of sides of right tri are given perpendicular to hypotenuse is (perpendicular*base)/hypotenuse

[@RealMikeDobbs]

Hey, thanks for watching. I'm not sure what you are saying here. You seem to be defining the altitude in terms of itself. Are you able to clarify?

[@MKangu]

Thanks brother 😊 new subscriber i am

[@RealMikeDobbs]

Thanks so much! Glad you found it helpful 😀

[@t4_y858]

Nice video

[@RealMikeDobbs]

Thanks so much 😀

[@Numbers-n-Innovations]

Thank you

[@RealMikeDobbs]

You’re very welcome 😀

[@Numbers-n-Innovations]

@@RealMikeDobbs you really explained it very well. I saw two other videos as well but you are awesome. Thank you for such great video.

[@RealMikeDobbs]

Thanks so much for the feedback! So glad you found it helpful.

[@geraldhartman2336]

Every example is knowledge of the hypotenuse. What if you know nothing about the hypotenuse, but know the 2 legs - “A” & “B”? How do u solve for the altitude?

[@RealMikeDobbs]

Thanks for watching. In that case, use Pythag to find the hypotenuse and then proceed as shown in the video. Remember, anytime you have two legs of a rt triangle you can always find the 3rd with Pythag 😄

[@johnnyramales2450]

perfect

[@RealMikeDobbs]

Thanks Johnny 😄

[@christopherellis2663]

THALES, 18×2=X², 20+16=36, x=6. Why do you think it necessary to use the complicated process? 6²+2²=a², 6²+18²=b²

[@RealMikeDobbs]

I don't follow your comment. You say THALES, which I presume is meant to invoke THALES' theorem, but that is not needed since we already know it is a right triangle. Your first equation is the one I solved to find x in the video- I am not sure what your second equation is meant to represent (20 + 16 = 36). IF we needed to solve for the remaining sides of the larger triangle (which we don't), I would use Pythag as you suggest in your final two equations. What is the complicated process to which you refer?