Class Triangle

A triangle ABC of the plane. Built from three points, three lines, or six coordinates. It gives the sides, the angles and the remarkable lines (medians, heights, mediators, bisectors) with exact coordinates. tex and display are not available: describe a triangle through its vertices or its lines.

Example

new Triangle(new Point(0, 0), new Point(4, 0), new Point(0, 3)).isRectangle() // true

Implements

IPiMathObject<Triangle>

Index

Constructors

constructor

Accessors

A AB AC asDegree asRadians B BA BC C CA CB display isValid lines remarquables tex

Constructors

constructor

new Triangle(...values: unknown[]): Triangle
Parameters
- ...values: unknown[]
Returns Triangle
- Defined in src/geometry/triangle.ts:29

Accessors

A

get A(): Point
Vertex A. Setting a vertex refreshes the validity and the remarkable lines.

Returns Point
- Defined in src/geometry/triangle.ts:115
set A(value: Point): void
Parameters
- value: Point
Returns void
- Defined in src/geometry/triangle.ts:119

AB

get AB(): Vector
The vector from A to B.

Returns Vector
- Defined in src/geometry/triangle.ts:128

AC

get AC(): Vector
The vector from A to C.

Returns Vector
- Defined in src/geometry/triangle.ts:135

asDegree

get asDegree(): this
Output option: getAngle gives degrees. Chainable, persistent.

Returns this
- Defined in src/geometry/triangle.ts:196

asRadians

get asRadians(): this
Output option: getAngle gives radians (default). Chainable, persistent.

Returns this
- Defined in src/geometry/triangle.ts:204

B

get B(): Point
Vertex B. Setting a vertex refreshes the validity and the remarkable lines.

Returns Point
- Defined in src/geometry/triangle.ts:142
set B(value: Point): void
Parameters
- value: Point
Returns void
- Defined in src/geometry/triangle.ts:146

BA

get BA(): Vector
The vector from B to A.

Returns Vector
- Defined in src/geometry/triangle.ts:155

BC

get BC(): Vector
The vector from B to C.

Returns Vector
- Defined in src/geometry/triangle.ts:162

C

get C(): Point
Vertex C. Setting a vertex refreshes the validity and the remarkable lines.

Returns Point
- Defined in src/geometry/triangle.ts:169
set C(value: Point): void
Parameters
- value: Point
Returns void
- Defined in src/geometry/triangle.ts:173

CA

get CA(): Vector
The vector from C to A.

Returns Vector
- Defined in src/geometry/triangle.ts:182

CB

get CB(): Vector
The vector from C to B.

Returns Vector
- Defined in src/geometry/triangle.ts:189

display

get display(): string
Not implemented on purpose: see tex.

Returns string

Throws
always.
Implementation of IPiMathObject.display
- Defined in src/geometry/triangle.ts:88

isValid

get isValid(): boolean
False when the three vertices are collinear.

Returns boolean
- Defined in src/geometry/triangle.ts:470

lines

get lines(): Record<TriangleSide, Line>
The lines of the sides, as {AB, BC, AC}.

Returns Record<TriangleSide, Line>
- Defined in src/geometry/triangle.ts:477

remarquables

get remarquables(): RemarquableLines
The remarkable lines already computed. An entry is null until the matching get*** method is called.

Returns RemarquableLines
- Defined in src/geometry/triangle.ts:492

tex

get tex(): string
Not implemented on purpose: a triangle has no single equation to display.

Returns string

Throws
always. Describe it through its lines or its vertices.
Implementation of IPiMathObject.tex
- Defined in src/geometry/triangle.ts:82

Methods

clone

clone(): this
Full duplicate of this instance, including display state (selected form and options set via as*** / with***). Distinct from copy.

Returns this
Implementation of IPiMathObject.clone
- Defined in src/geometry/triangle.ts:90

copy

copy(value: Triangle): this
Copies the three vertices from value into this instance. Math state only — #radians is not transferred (use clone for a full copy).
Parameters
- value: Triangle
Returns this
Implementation of IPiMathObject.copy
- Defined in src/geometry/triangle.ts:104

getAngle

getAngle(name: "A" | "B" | "C"): number
Angle at a vertex, as a decimal number: in radians by default, in degrees after asDegree.
Parameters
- name: "A" | "B" | "C"
Returns number
- Defined in src/geometry/triangle.ts:282

getBisectors

getBisectors(
internal?: boolean,
): { A: Line; B: Line; C: Line; intersection: Point | null }
The bisectors of the angles, as {A, B, C, intersection}, where intersection is their common point.
Parameters
- internal: boolean = true
  true (default) for the internal bisectors, false for the external ones.
Returns { A: Line; B: Line; C: Line; intersection: Point | null }

Throws
if the triangle is degenerate.
- Defined in src/geometry/triangle.ts:303

getHeights

getHeights(): { A: Line; B: Line; C: Line; intersection: Point | null }
The heights, as {A, B, C, intersection}, where intersection is the orthocenter.

Returns { A: Line; B: Line; C: Line; intersection: Point | null }

Throws
if the triangle is degenerate.
- Defined in src/geometry/triangle.ts:328

getMedians

getMedians(): { A: Line; B: Line; C: Line; intersection: Point | null }
The medians, as {A, B, C, intersection}, where intersection is the centroid.

Returns { A: Line; B: Line; C: Line; intersection: Point | null }

Throws
if the triangle is degenerate.
- Defined in src/geometry/triangle.ts:348

getMediators

getMediators(): { a: Line; b: Line; c: Line; intersection: Point | null }
The perpendicular bisectors of the sides, as {a, b, c, intersection}, where intersection is the circumcenter.

Returns { a: Line; b: Line; c: Line; intersection: Point | null }

Throws
if the triangle is degenerate.
- Defined in src/geometry/triangle.ts:369

getMiddles

getMiddles(): { AB: Point; AC: Point; BC: Point }
The midpoints of the sides, as {AB, AC, BC}.

Returns { AB: Point; AC: Point; BC: Point }
- Defined in src/geometry/triangle.ts:389

getPoints

getPoints(): Point[]
The vertices [A, B, C].

Returns Point[]
- Defined in src/geometry/triangle.ts:400

getSortedPoints

getSortedPoints(): Point[]
The vertices sorted by x, then by y.

Returns Point[]
- Defined in src/geometry/triangle.ts:407

isEqual

isEqual(T: Triangle): boolean
True when both triangles have the same vertices, whatever their order.
Parameters
- T: Triangle
Returns boolean
- Defined in src/geometry/triangle.ts:418

isEquilateral

isEquilateral(): boolean
True when the three sides have the same length.

Returns boolean
- Defined in src/geometry/triangle.ts:431

isIsocele

isIsocele(): boolean
True when two sides have the same length.

Returns boolean
- Defined in src/geometry/triangle.ts:444

isRectangle

isRectangle(): boolean
True when two sides are perpendicular.

Returns boolean
- Defined in src/geometry/triangle.ts:459

parse

parse(...values: unknown[]): this
Replace the triangle with a triangle, three lines (objects or equation strings), three points, or six coordinates.
Parameters
- ...values: unknown[]
Returns this

Throws
if one of six values is not a number.

Throws
if the points are collinear or the lines do not form a triangle.
- Defined in src/geometry/triangle.ts:42

reset

reset(): this
Recompute the validity and forget the cached lines and remarkable lines. This is done automatically when a vertex changes through its setter or its x and y coordinates.

Returns this
- Defined in src/geometry/triangle.ts:500

`Static`fromCoordinates

fromCoordinates(
    x1: InputValue<Fraction>,
    y1: InputValue<Fraction>,
    x2: InputValue<Fraction>,
    y2: InputValue<Fraction>,
    x3: InputValue<Fraction>,
    y3: InputValue<Fraction>,
): Triangle
Build a triangle from the coordinates of its three vertices.
Parameters
- x1: InputValue<Fraction>
- y1: InputValue<Fraction>
- x2: InputValue<Fraction>
- y2: InputValue<Fraction>
- x3: InputValue<Fraction>
- y3: InputValue<Fraction>
Returns Triangle

Throws
if the points are collinear or two of them are the same.
- Defined in src/geometry/triangle.ts:213

`Static`fromLines

fromLines(
    line1: string | Line,
    line2: string | Line,
    line3: string | Line,
): Triangle
Build a triangle from the lines of its sides AB, BC and AC, given as lines or equation strings.
Parameters
- line1: string | Line
- line2: string | Line
- line3: string | Line
Returns Triangle

Throws
if two lines are parallel or the lines do not form a triangle.
- Defined in src/geometry/triangle.ts:229

`Static`fromPoints

fromPoints(A: Point, B: Point, C: Point): Triangle
Build a triangle from its three vertices.
Parameters
- A: Point
- B: Point
- C: Point
Returns Triangle

Throws
if the points are collinear or two of them are the same.
- Defined in src/geometry/triangle.ts:267

Class Triangle

Example

Implements

Index

Constructors

Accessors

Methods

Constructors

constructor

Parameters

Returns Triangle

Accessors

A

Returns Point

Parameters

Returns void

AB

Returns Vector

AC

Returns Vector

asDegree

Returns this

asRadians

Returns this

B

Returns Point

Parameters

Returns void

BA

Returns Vector

BC

Returns Vector

C

Returns Point

Parameters

Returns void

CA

Returns Vector

CB

Returns Vector

display

Returns string

Throws

isValid

Returns boolean

lines

Returns Record<TriangleSide, Line>

remarquables

Returns RemarquableLines

tex

Returns string

Throws

Methods

clone

Returns this

copy

Parameters

Returns this

getAngle

Parameters

Returns number

getBisectors

Parameters

Returns { A: Line; B: Line; C: Line; intersection: Point | null }

Throws

getHeights

Returns { A: Line; B: Line; C: Line; intersection: Point | null }

Throws

getMedians

Returns { A: Line; B: Line; C: Line; intersection: Point | null }

Throws

getMediators

Returns { a: Line; b: Line; c: Line; intersection: Point | null }

Throws

getMiddles

Returns { AB: Point; AC: Point; BC: Point }

getPoints

Returns Point[]

getSortedPoints

Returns Point[]

`Static`fromCoordinates

`Static`fromLines

`Static`fromPoints