Elearn Geometry Problem 225: Viviani Theorem Extension

Regular Polygon, Apothem, Distance
In a regular n-sided polygon, the sum of the perpendicular distances from an interior point to the n sides being n times the apothem of the polygon.



See complete Problem 225 at:
gogeometry.com/problem/p225_viviani_theorem_regular_polygon.htm

Level: High School, SAT Prep, College geometry

Elearn Geometry Problem 224: Viviani Theorem, Isosceles Triangle

Altitude, Distance, Point on the extension of the base
In an isosceles triangle ABC (AB = BC), the sum of the distances from any point on the extension of CA to the equal sides is equal to the altitude of the equal sides.



See complete Problem 224 at:
gogeometry.com/problem/p224_viviani_theorem_isosceles_triangle.htm

Level: High School, SAT Prep, College geometry

Elearn Geometry Problem 223: Viviani Theorem, Isosceles Triangle

Altitude, Distance
In an isosceles triangle ABC (AB = BC), the sum of the distances from any point on AC to the equal sides is equal to the altitude of the equal sides.



See complete Problem 223 at:
gogeometry.com/problem/p223_viviani_theorem_isosceles_triangle.htm

Level: High School, SAT Prep, College geometry

Elearn Geometry Problem 222: Viviani Theorem, Exterior point

Equilateral Triangle, Exterior Point
For a given point D outside an equilateral triangle ABC, the sum of the distances DE and DF minus DG from the point D to the sides BC, AB and AC respectively is equal to the altitude of the triangle.



See complete Problem 222 at:
gogeometry.com/problem/p222_viviani_theorem_equilateral_triangle_exterior.htm

Level: High School, SAT Prep, College geometry

Elearn Geometry Problem 221: Viviani Theorem

Equilateral Triangle, Interior Point
In an equilateral triangle, prove that the sum of the distances from any interior point to the sides is equal to the altitude of the triangle.



See complete Problem 221 at:
gogeometry.com/problem/p221_viviani_theorem_equilateral_triangle.htm

Level: High School, SAT Prep, College geometry