EasyGeometry::D2::Triangle

A polygon with three vertices and three sides. Line inherit from Linear Entity.

#is_similar?(other)

Is another triangle similar to this one.

#is_equilateral?

Are all the sides the same length?

Precision - 10e-13

#is_isosceles?

Are two or more of the sides the same length?

Precision - 10e-13

#is_scalene?

Are all the sides of the triangle of different lengths?

Precision - 10e-13

#is_right?

Is the triangle right-angled.

#altitudes

The altitudes of the triangle.

An altitude of a triangle is a segment through a vertex, perpendicular to the opposite side, with length being the height of the vertex measured from the line containing the side.

t1 = EasyGeometry::D2::Triangle.new([0, 0], [5, 0], [0, 5])

t1.altitudes # {
             #    Point(0, 0): Segment(Point(0, 0), Point(5/2, 5/2)),
             #    Point(5, 0): Segment(Point(5, 0), Point(0, 0)),
             #    Point(0, 5): Segment(Point(0, 5), Point(0, 0)),
             # }

#orthocenter

The orthocenter of the triangle.

The orthocenter is the intersection of the altitudes of a triangle. It may lie inside, outside or on the triangle.

#circumcenter

The circumcenter of the triangle.

The circumcenter is the center of the circumcircle.

#circumradius

The radius of the circumcircle of the triangle.

#bisectors

The angle bisectors of the triangle.

An angle bisector of a triangle is a straight line through a vertex which cuts the corresponding angle in half.

t1 = EasyGeometry::D2::Triangle.new([0, 0], [5, 0], [0, 5])

t1.altitudes # {
             #    Point(0, 0): Segment(Point(0, 0), Point(5/2, 5/2)),
             #    Point(5, 0): Segment(Point(5, 0), Point(0, 585786437626905/282842712474619)),
             #    Point(0, 5): Segment(Point(0, 5), Point(585786437626905/282842712474619, 0)),
             # }

#incenter

The center of the incircle.

The incircle is the circle which lies inside the triangle and touches all three sides.

#inradius

The radius of the incircle.

#exradii

The radius of excircles of a triangle.

An excircle of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two.

[1] http://mathworld.wolfram.com/Exradius.html

[2] http://mathworld.wolfram.com/Excircles.html

t1 = EasyGeometry::D2::Triangle.new([0, 0], [5, 0], [0, 5])

t1.exradii # {
             #    Segment(Point(0, 0), Point(5, 0)): 3.5355339059327373,
             #    Segment(Point(5, 0), Point(0, 5)): 8.535533905932738,
             #    Segment(Point(0, 5), Point(0, 0)): 3.5355339059327373,
             # }

#medians

The medians of the triangle.

A median of a triangle is a straight line through a vertex and the midpoint of the opposite side, and divides the triangle into two equal areas.

t1 = EasyGeometry::D2::Triangle.new([0, 0], [1, 0], [0, 1])

t1.medians # {
             #    Point(0, 0): Segment(Point(0, 0), Point(0.5, 0.5)),
             #    Point(1, 0): Segment(Point(1, 0), Point(0, 0.5)),
             #    Point(0, 1): Segment(Point(0, 1), Point(0.5, 0)),
             # }

#medial

The medial triangle of the triangle.

The triangle which is formed from the midpoints of the three sides.

#eulerline

The Euler line of the triangle.

The line which passes through circumcenter, centroid and orthocenter.

PreviousEasyGeometry::D2::Polygon

Last updated 6 years ago

hashtag#is_similar?(other)

hashtag#is_equilateral?

hashtag#is_isosceles?

hashtag#is_scalene?

hashtag#is_right?

hashtag#altitudes

hashtag#orthocenter

hashtag#circumcenter

hashtag#circumradius

hashtag#bisectors

hashtag#incenter

hashtag#inradius

hashtag#exradii

hashtag#medians

hashtag#medial

hashtag#eulerline

#is_similar?(other)

#is_equilateral?

#is_isosceles?

#is_scalene?

#is_right?

#altitudes

#orthocenter

#circumcenter

#circumradius

#bisectors

#incenter

#inradius

#exradii

#medians

#medial

#eulerline