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Updated Mar 18, 2026
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Trojuholník – typy a vlastnosti
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Čo je trojuholník a prečo je dôležitý
Každý deň vidíš desiatky trojuholníkov a možno si to ani neuvedomuješ. Trojuholník je geometrický útvar s troma stranami, troma vrcholmi a troma uhlami - nič viac, nič menej.
Zapamätaj si toto označovanie: vrcholy pomenúvame veľkými písmenami (A, B, C), strany malými písmenami oproti vrcholu (a, b, c). Každý trojuholník má tri vnútorné uhly, ktoré označujeme gréckymi písmenami α (alfa), β (beta) a γ (gama).
Najdôležitejšie pravidlo, ktoré musíš vedieť naspamäť: súčet všetkých troch uhlov je vždy 180°. Toto platí pre každý trojuholník na svete - α + β + γ = 180°.
Tip pre skúšku: Ak poznáš dva uhly trojuholníka, tretí vždy vypočítaš ako 180° minus súčet tých dvoch známych!
Delenie trojuholníkov podle dlžky strán
Môžeme rozdeliť trojuholníky podľa toho, aké dlhé majú strany. Toto rozdelenie je super jednoduché a logické.
Rôznostranný trojuholník má všetky tri strany rôzne dlhé. Logicky teda aj všetky tri uhly budú mať rôznu veľkosť. Je to asi najčastejší typ trojuholníka, s ktorým sa stretneme.
Rovnoramenný trojuholník má dve strany rovnako dlhé - nazývame ich ramená. Tretia strana je základňa. Tu platí cool pravidlo: uhly pri základni sú vždy rovnako veľké!
Rovnostranný trojuholník je najšpeciálnejší - všetky tri strany majú rovnakú dĺžku. To znamená, že aj všetky tri uhly sú rovnaké, každý má presne 60° (180° ÷ 3 = 60°).
Pamätka: Rovnostranný trojuholník je vlastne špeciálny prípad rovnoramenného - má tri ramená namiesto dvoch!
Delenie trojuholníkov podle veľkosti uhlov
Teraz sa pozrime na trojuholníky z pohľadu ich uhlov. Toto rozdelenie je kľúčové pre riešenie úloh.
Pravouhlý trojuholník má jeden pravý uhol (presne 90°). Strana oproti pravému uhlu sa volá prepona a je vždy najdlhšia. Ostatné dve strany sú odvesny. Pravé uhly vidíš všade - na rohoch stola, okien, či dverí.
Ostrouhlý trojuholník má všetky tri uhly ostré, teda menšie ako 90°. Je to taký "štíhly" trojuholník bez tupých rohov.
Tupouhlý trojuholník má jeden tupý uhol (väčší ako 90°). Pozor - nikdy nemôže mať dva tupé uhly, lebo by súčet už bol viac ako 180°!
Skúšková otázka: Keď vidíš v úlohe uhol 90°, hneď vieš, že ide o pravouhlý trojuholník a prepona je oproti tomuto uhlu!
Riešené príklady krok za krokom
Poďme si ukázať, ako sa to robí v praxi. Tieto typy úloh sa často objavujú na testoch.
Príklad 1: Máš trojuholník so stranami 6 cm, 8 cm, 10 cm a uhlami 30°, 60°, 90°. Aký je to trojuholník? Podľa strán: všetky rôzne = rôznostranný. Podľa uhlov: jeden je 90° = pravouhlý. Odpoveď: rôznostranný pravouhlý trojuholník.
Príklad 2: V trojuholníku sú dva uhly 45° a 75°. Aký je tretí? Použiješ vzorec: 180° - 45° - 75° = 60°. Jednoduchšie to už nie je!
Príklad 3: Rovnoramenný trojuholník má uhol medzi ramenami 40°. Aké sú uhly pri základni? Keďže sú rovnaké, označme ich x. Potom: 40° + x + x = 180°, takže 2x = 140°, teda x = 70°.
Trik pre úspech: Vždy si nakreslime trojuholník a vyznač známe údaje - vizuálne ti pomôže vidieť riešenie!
Dôležité tipy a zhrnutie
Tu máš všetko, co potrebuješ vedieť na perfektnú známku z trojuholníkov.
Základné pravidlá: Súčet uhlov = 180°, vrcholy označujeme veľkými písmenami, strany malými. V pravouhlom trojuholníku je prepona vždy najdlhšia a leží oproti pravému uhlu.
Typy podľa strán: Rôznostranný (všetky strany rôzne), rovnoramenný (dve strany rovnaké), rovnostranný (všetky strany rovnaké, všetky uhly 60°).
Typy podľa uhlov: Pravouhlý (jeden uhol 90°), ostrouhlý (všetky uhly < 90°), tupouhlý (jeden uhol > 90°). Trojuholník môže byť napríklad rovnoramenný a zároveň pravouhlý!
Záverečný tip: Vždy si urob náčrt trojuholníka a vyznač všetky známe údaje. Polovica úlohy je už vyriešená, keď vidíš, s čím pracuješ!
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.
Most popular content in Matematika
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Can't find what you're looking for? Explore other subjects.
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
Trojuholník – typy a vlastnosti
Trojuholníky sú všade okolo nás - od strechy domu po značky na ceste. Poznať ich typy a vlastnosti ti pomôže nielen v matematike, ale aj v každodennom živote. Poďme si ukázať, aké jednoduché je rozlíšiť rôzne druhy trojuholníkov!
Čo je trojuholník a prečo je dôležitý
Každý deň vidíš desiatky trojuholníkov a možno si to ani neuvedomuješ. Trojuholník je geometrický útvar s troma stranami, troma vrcholmi a troma uhlami - nič viac, nič menej.
Zapamätaj si toto označovanie: vrcholy pomenúvame veľkými písmenami (A, B, C), strany malými písmenami oproti vrcholu (a, b, c). Každý trojuholník má tri vnútorné uhly, ktoré označujeme gréckymi písmenami α (alfa), β (beta) a γ (gama).
Najdôležitejšie pravidlo, ktoré musíš vedieť naspamäť: súčet všetkých troch uhlov je vždy 180°. Toto platí pre každý trojuholník na svete - α + β + γ = 180°.
Tip pre skúšku: Ak poznáš dva uhly trojuholníka, tretí vždy vypočítaš ako 180° minus súčet tých dvoch známych!
Sign up to see the contentIt's free!
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Delenie trojuholníkov podle dlžky strán
Môžeme rozdeliť trojuholníky podľa toho, aké dlhé majú strany. Toto rozdelenie je super jednoduché a logické.
Rôznostranný trojuholník má všetky tri strany rôzne dlhé. Logicky teda aj všetky tri uhly budú mať rôznu veľkosť. Je to asi najčastejší typ trojuholníka, s ktorým sa stretneme.
Rovnoramenný trojuholník má dve strany rovnako dlhé - nazývame ich ramená. Tretia strana je základňa. Tu platí cool pravidlo: uhly pri základni sú vždy rovnako veľké!
Rovnostranný trojuholník je najšpeciálnejší - všetky tri strany majú rovnakú dĺžku. To znamená, že aj všetky tri uhly sú rovnaké, každý má presne 60° (180° ÷ 3 = 60°).
Pamätka: Rovnostranný trojuholník je vlastne špeciálny prípad rovnoramenného - má tri ramená namiesto dvoch!
Sign up to see the contentIt's free!
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Delenie trojuholníkov podle veľkosti uhlov
Teraz sa pozrime na trojuholníky z pohľadu ich uhlov. Toto rozdelenie je kľúčové pre riešenie úloh.
Pravouhlý trojuholník má jeden pravý uhol (presne 90°). Strana oproti pravému uhlu sa volá prepona a je vždy najdlhšia. Ostatné dve strany sú odvesny. Pravé uhly vidíš všade - na rohoch stola, okien, či dverí.
Ostrouhlý trojuholník má všetky tri uhly ostré, teda menšie ako 90°. Je to taký "štíhly" trojuholník bez tupých rohov.
Tupouhlý trojuholník má jeden tupý uhol (väčší ako 90°). Pozor - nikdy nemôže mať dva tupé uhly, lebo by súčet už bol viac ako 180°!
Skúšková otázka: Keď vidíš v úlohe uhol 90°, hneď vieš, že ide o pravouhlý trojuholník a prepona je oproti tomuto uhlu!
Sign up to see the contentIt's free!
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Riešené príklady krok za krokom
Poďme si ukázať, ako sa to robí v praxi. Tieto typy úloh sa často objavujú na testoch.
Príklad 1: Máš trojuholník so stranami 6 cm, 8 cm, 10 cm a uhlami 30°, 60°, 90°. Aký je to trojuholník? Podľa strán: všetky rôzne = rôznostranný. Podľa uhlov: jeden je 90° = pravouhlý. Odpoveď: rôznostranný pravouhlý trojuholník.
Príklad 2: V trojuholníku sú dva uhly 45° a 75°. Aký je tretí? Použiješ vzorec: 180° - 45° - 75° = 60°. Jednoduchšie to už nie je!
Príklad 3: Rovnoramenný trojuholník má uhol medzi ramenami 40°. Aké sú uhly pri základni? Keďže sú rovnaké, označme ich x. Potom: 40° + x + x = 180°, takže 2x = 140°, teda x = 70°.
Trik pre úspech: Vždy si nakreslime trojuholník a vyznač známe údaje - vizuálne ti pomôže vidieť riešenie!
Sign up to see the contentIt's free!
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Dôležité tipy a zhrnutie
Tu máš všetko, co potrebuješ vedieť na perfektnú známku z trojuholníkov.
Základné pravidlá: Súčet uhlov = 180°, vrcholy označujeme veľkými písmenami, strany malými. V pravouhlom trojuholníku je prepona vždy najdlhšia a leží oproti pravému uhlu.
Typy podľa strán: Rôznostranný (všetky strany rôzne), rovnoramenný (dve strany rovnaké), rovnostranný (všetky strany rovnaké, všetky uhly 60°).
Typy podľa uhlov: Pravouhlý (jeden uhol 90°), ostrouhlý (všetky uhly < 90°), tupouhlý (jeden uhol > 90°). Trojuholník môže byť napríklad rovnoramenný a zároveň pravouhlý!
Záverečný tip: Vždy si urob náčrt trojuholníka a vyznač všetky známe údaje. Polovica úlohy je už vyriešená, keď vidíš, s čím pracuješ!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
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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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