Pytagorova veta je jedna z najužitočnejších vecí v matematike, ktorú... Show more
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Updated Mar 25, 2026
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Pytagorova veta: Jednoduchý sprievodca s vysvetleniami
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Čo je Pytagorova veta a základné pojmy
Zapamätaj si hneď na začiatku - Pytagorova veta funguje len v pravouhlých trojuholníkoch! Žiadne iné trojuholníky, len tie s jedným 90° uhlom.
V pravouhlom trojuholníku máš tri strany s vlastnými menami. Odvesny (označujeme ich a a b) sú tie dve kratšie strany, ktoré sa stretávajú v pravom uhle. Prepona (označujeme ju c) je vždy tá najdlhšia strana - leží oproti pravému uhlu.
Pytagorova veta je vlastne jednoduchá formula: a² + b² = c². Znamená to, že ak si vezmeš dĺžky oboch odvesien, umocníš ich na druhú a sčítaš, dostaneš druhú mocninu prepony.
💡 Tip: Druhá mocnina znamená číslo krát samo seba (3² = 3×3 = 9). Druhá odmocnina je opačná operácia (√9 = 3).
Ako vypočítať preponu
Keď poznáš obe odvesny a chceš zistiť dĺžku prepony, postup je priamočiary. Vezmi si konkrétny príklad - odvesny majú 3 cm a 4 cm.
Najprv napíš vzorec: a² + b² = c². Potom dosaď čísla: 3² + 4² = c². Vypočítaj mocniny: 9 + 16 = c². Sčítaj: 25 = c².
Nakoniec musíš odmocniť výsledok: c = √25 = 5 cm. Hotovo! Prepona meria 5 cm.
Vždy si skontroluj, či ti vyšla prepona dlhšia ako odvesny - ak nie, urobil si niekde chybu.
💡 Kontrola: Prepona musí byť vždy najdlhšia strana trojuholníka!
Ako vypočítať odvesnu
Keď poznáš preponu a jednu odvesnu, môžeš ľahko vypočítať tú druhú odvesnu. Napríklad máš preponu 10 m a jednu odvesnu 6 m.
Začni s vzorcom a² + b² = c² a dosaď známe hodnoty: 6² + b² = 10². Vypočítaj mocniny: 36 + b² = 100.
Teraz preusporiadas vzorec, aby si dostal b² samotné: b² = 100 - 36 = 64. Nakoniec odmocni: b = √64 = 8 m.
Kľúčové je správne preusporiadanie - vždy odčítavaš druhú mocninu menšej strany od väčšej.
💡 Pamätaj: Pri hľadaní odvesny vždy odčítavaš od prepony!
Praktické použitie v reálnom živote
Predstav si, že máš rebrík dlhý 5 metrov oprety o stenu. Spodok rebríka je 3 metre od steny - do akej výšky rebrík dosahuje?
Toto je praktická úloha s Pytagorovou vetou. Rebrík je prepona , vzdialenosť od steny je odvesna a výška na stene je druhá odvesna .
Použi vzorec: 3² + b² = 5². Vypočítaj: 9 + b² = 25. Preusporiadaj: b² = 25 - 9 = 16. Odmocni: b = √16 = 4 m.
Rebrík teda dosahuje do výšky 4 metre na stene. Takto môžeš riešiť množstvo praktických problémov!
💡 Tip na úspech: Vždy si najprv nakresli obrázok a označ si strany a, b, c.
Dôležité tipy a časté chyby
Najčastejšia chyba: Používanie Pytagorovej vety na trojuholníky, ktoré nie sú pravouhlé. Vždy si najprv over, že má trojuholník 90° uhol!
Pri riešení úloh si vždy nakresli obrázek a označ si strany. Pomôže ti to vyhnúť sa zámenám medzi odvesnami a preponou. Nezabúdaj na jednotky - ak počítaš v centimetroch, výsledok bude v centimetroch.
Užitočná kontrola: Pytagorovu vetu môžeš použiť aj naopak. Ak pre tri strany trojuholníka platí a² + b² = c², tak je trojuholník určite pravouhlý.
Pamätaj si základný postup: napíš vzorec, dosaď známe hodnoty, vypočítaj mocniny, vyriešs rovnicu a na konci odmocni.
💡 Záverečný tip: Cvič si na jednoduchých číslach ako 3-4-5 alebo 6-8-10. Tieto "pythagorovské trojice" ti pomôžu pochopiť princíp.
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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
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This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
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Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
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Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Pytagorova veta: Jednoduchý sprievodca s vysvetleniami
Pytagorova veta je jedna z najužitočnejších vecí v matematike, ktorú budeš používať nielen v škole, ale aj v bežnom živote. Pomôže ti vypočítať neznáme dĺžky v pravouhlých trojuholníkoch - či už riešiš domácu úlohu alebo zisťuješ, či sa ti nový... Show more
Čo je Pytagorova veta a základné pojmy
Zapamätaj si hneď na začiatku - Pytagorova veta funguje len v pravouhlých trojuholníkoch! Žiadne iné trojuholníky, len tie s jedným 90° uhlom.
V pravouhlom trojuholníku máš tri strany s vlastnými menami. Odvesny (označujeme ich a a b) sú tie dve kratšie strany, ktoré sa stretávajú v pravom uhle. Prepona (označujeme ju c) je vždy tá najdlhšia strana - leží oproti pravému uhlu.
Pytagorova veta je vlastne jednoduchá formula: a² + b² = c². Znamená to, že ak si vezmeš dĺžky oboch odvesien, umocníš ich na druhú a sčítaš, dostaneš druhú mocninu prepony.
💡 Tip: Druhá mocnina znamená číslo krát samo seba (3² = 3×3 = 9). Druhá odmocnina je opačná operácia (√9 = 3).
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Ako vypočítať preponu
Keď poznáš obe odvesny a chceš zistiť dĺžku prepony, postup je priamočiary. Vezmi si konkrétny príklad - odvesny majú 3 cm a 4 cm.
Najprv napíš vzorec: a² + b² = c². Potom dosaď čísla: 3² + 4² = c². Vypočítaj mocniny: 9 + 16 = c². Sčítaj: 25 = c².
Nakoniec musíš odmocniť výsledok: c = √25 = 5 cm. Hotovo! Prepona meria 5 cm.
Vždy si skontroluj, či ti vyšla prepona dlhšia ako odvesny - ak nie, urobil si niekde chybu.
💡 Kontrola: Prepona musí byť vždy najdlhšia strana trojuholníka!
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Ako vypočítať odvesnu
Keď poznáš preponu a jednu odvesnu, môžeš ľahko vypočítať tú druhú odvesnu. Napríklad máš preponu 10 m a jednu odvesnu 6 m.
Začni s vzorcom a² + b² = c² a dosaď známe hodnoty: 6² + b² = 10². Vypočítaj mocniny: 36 + b² = 100.
Teraz preusporiadas vzorec, aby si dostal b² samotné: b² = 100 - 36 = 64. Nakoniec odmocni: b = √64 = 8 m.
Kľúčové je správne preusporiadanie - vždy odčítavaš druhú mocninu menšej strany od väčšej.
💡 Pamätaj: Pri hľadaní odvesny vždy odčítavaš od prepony!
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Praktické použitie v reálnom živote
Predstav si, že máš rebrík dlhý 5 metrov oprety o stenu. Spodok rebríka je 3 metre od steny - do akej výšky rebrík dosahuje?
Toto je praktická úloha s Pytagorovou vetou. Rebrík je prepona , vzdialenosť od steny je odvesna a výška na stene je druhá odvesna .
Použi vzorec: 3² + b² = 5². Vypočítaj: 9 + b² = 25. Preusporiadaj: b² = 25 - 9 = 16. Odmocni: b = √16 = 4 m.
Rebrík teda dosahuje do výšky 4 metre na stene. Takto môžeš riešiť množstvo praktických problémov!
💡 Tip na úspech: Vždy si najprv nakresli obrázok a označ si strany a, b, c.
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Improve your grades
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Dôležité tipy a časté chyby
Najčastejšia chyba: Používanie Pytagorovej vety na trojuholníky, ktoré nie sú pravouhlé. Vždy si najprv over, že má trojuholník 90° uhol!
Pri riešení úloh si vždy nakresli obrázek a označ si strany. Pomôže ti to vyhnúť sa zámenám medzi odvesnami a preponou. Nezabúdaj na jednotky - ak počítaš v centimetroch, výsledok bude v centimetroch.
Užitočná kontrola: Pytagorovu vetu môžeš použiť aj naopak. Ak pre tri strany trojuholníka platí a² + b² = c², tak je trojuholník určite pravouhlý.
Pamätaj si základný postup: napíš vzorec, dosaď známe hodnoty, vypočítaj mocniny, vyriešs rovnicu a na konci odmocni.
💡 Záverečný tip: Cvič si na jednoduchých číslach ako 3-4-5 alebo 6-8-10. Tieto "pythagorovské trojice" ti pomôžu pochopiť princíp.
Sign up to see the contentIt's free!
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Join milions of students
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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Students love us — and so will you.
4.6/5
App Store
4.7/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user