The World Of The World Of TrianglesTriangles

Juliána MelicherováUniversity of Pavol Jozef Šafárik, Košice

TrianglesTriangles

• 3-sided polygon• three sides and

three angles• together the

three angles equal 180°

Triangle Inequality Triangle Inequality

TheoremTheorem

• any side of a triangle is always shorter than the sum of the other two sides

Acute TrianglesAcute Triangles

• all three angles are less than 90°

Obtuse TrianglesObtuse Triangles

• one of the angles is greater than 90°

Right TrianglesRight Triangles

• with an angle of 90°

Scalene TrianglesScalene Triangles

• three unequal sides

Isosceles TrianglesIsosceles Triangles

• with (at least) two equal sides

Isosceles Triangle Isosceles Triangle

Theorem Theorem

• if two sides of a triangle are congruent, the angles opposite them are congruent

Equilateral Equilateral TrianglesTriangles

• with all three sides of equal length

Equiangular Equiangular TrianglesTriangles

• which has three equal angles

Congruent Congruent TrianglesTriangles

• triangles whose corresponding angles and sides are congruent 

• the same size and shape.

The HypotenuseThe Hypotenuse

• the triangle's longest side, i.e., the side opposite the right angle.

The Pythagorean The Pythagorean TheoremTheorem

• for a right triangle with legs a and b and hypotenuse c, a2+b2=c2.

Penrose trianglePenrose triangle• impossible object

Thank you for your Thank you for your attention!attention!