the world of triangles juliána melicherová university of pavol jozef Šafárik, košice
TRANSCRIPT
![Page 1: The World Of Triangles Juliána Melicherová University of Pavol Jozef Šafárik, Košice](https://reader036.vdocument.in/reader036/viewer/2022082710/56649e745503460f94b73f72/html5/thumbnails/1.jpg)
The World Of The World Of TrianglesTriangles
Juliána MelicherováUniversity of Pavol Jozef Šafárik, Košice
![Page 2: The World Of Triangles Juliána Melicherová University of Pavol Jozef Šafárik, Košice](https://reader036.vdocument.in/reader036/viewer/2022082710/56649e745503460f94b73f72/html5/thumbnails/2.jpg)
TrianglesTriangles
• 3-sided polygon• three sides and
three angles• together the
three angles equal 180°
![Page 3: The World Of Triangles Juliána Melicherová University of Pavol Jozef Šafárik, Košice](https://reader036.vdocument.in/reader036/viewer/2022082710/56649e745503460f94b73f72/html5/thumbnails/3.jpg)
Triangle Inequality Triangle Inequality
TheoremTheorem
• any side of a triangle is always shorter than the sum of the other two sides
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Acute TrianglesAcute Triangles
• all three angles are less than 90°
![Page 5: The World Of Triangles Juliána Melicherová University of Pavol Jozef Šafárik, Košice](https://reader036.vdocument.in/reader036/viewer/2022082710/56649e745503460f94b73f72/html5/thumbnails/5.jpg)
Obtuse TrianglesObtuse Triangles
• one of the angles is greater than 90°
![Page 6: The World Of Triangles Juliána Melicherová University of Pavol Jozef Šafárik, Košice](https://reader036.vdocument.in/reader036/viewer/2022082710/56649e745503460f94b73f72/html5/thumbnails/6.jpg)
Right TrianglesRight Triangles
• with an angle of 90°
![Page 7: The World Of Triangles Juliána Melicherová University of Pavol Jozef Šafárik, Košice](https://reader036.vdocument.in/reader036/viewer/2022082710/56649e745503460f94b73f72/html5/thumbnails/7.jpg)
Scalene TrianglesScalene Triangles
• three unequal sides
![Page 8: The World Of Triangles Juliána Melicherová University of Pavol Jozef Šafárik, Košice](https://reader036.vdocument.in/reader036/viewer/2022082710/56649e745503460f94b73f72/html5/thumbnails/8.jpg)
Isosceles TrianglesIsosceles Triangles
• with (at least) two equal sides
![Page 9: The World Of Triangles Juliána Melicherová University of Pavol Jozef Šafárik, Košice](https://reader036.vdocument.in/reader036/viewer/2022082710/56649e745503460f94b73f72/html5/thumbnails/9.jpg)
Isosceles Triangle Isosceles Triangle
Theorem Theorem
• if two sides of a triangle are congruent, the angles opposite them are congruent
![Page 10: The World Of Triangles Juliána Melicherová University of Pavol Jozef Šafárik, Košice](https://reader036.vdocument.in/reader036/viewer/2022082710/56649e745503460f94b73f72/html5/thumbnails/10.jpg)
Equilateral Equilateral TrianglesTriangles
• with all three sides of equal length
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Equiangular Equiangular TrianglesTriangles
• which has three equal angles
![Page 12: The World Of Triangles Juliána Melicherová University of Pavol Jozef Šafárik, Košice](https://reader036.vdocument.in/reader036/viewer/2022082710/56649e745503460f94b73f72/html5/thumbnails/12.jpg)
Congruent Congruent TrianglesTriangles
• triangles whose corresponding angles and sides are congruent
• the same size and shape.
![Page 13: The World Of Triangles Juliána Melicherová University of Pavol Jozef Šafárik, Košice](https://reader036.vdocument.in/reader036/viewer/2022082710/56649e745503460f94b73f72/html5/thumbnails/13.jpg)
The HypotenuseThe Hypotenuse
• the triangle's longest side, i.e., the side opposite the right angle.
![Page 14: The World Of Triangles Juliána Melicherová University of Pavol Jozef Šafárik, Košice](https://reader036.vdocument.in/reader036/viewer/2022082710/56649e745503460f94b73f72/html5/thumbnails/14.jpg)
The Pythagorean The Pythagorean TheoremTheorem
• for a right triangle with legs a and b and hypotenuse c, a2+b2=c2.
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Penrose trianglePenrose triangle• impossible object
![Page 16: The World Of Triangles Juliána Melicherová University of Pavol Jozef Šafárik, Košice](https://reader036.vdocument.in/reader036/viewer/2022082710/56649e745503460f94b73f72/html5/thumbnails/16.jpg)
Thank you for your Thank you for your attention!attention!