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Quadrilateral, general

A plane figure enclosed by four lines is called a quadrilateral - do my homework for me . The four lines are the sides of the quadrilateral. Each two adjacent sides have a corner point in common.

If two lines have another point in common apart from the end points - https://domyhomework.club/math-problem-solver/ , the quadrilateral is called overlapped.

A quadrilateral is called convex if for every two points in the interior of the quadrilateral their connecting line is also completely in the interior of the quadrilateral. Otherwise the quadrilateral is called non-convex or concave.

The vertices of a (convex) quadrilateral are usually designated by capital letters - statistic homework help (e.g. A, B, C and D), the sides by small letters a, b, c and d, and the (interior) angles by α, β, γ and δ in the mathematical positive sense of revolution, unless the context requires other designations.

There are a and c as well as b and d opposite sides; a and b, b and c, c and d as well as d and a are adjacent sides.

The connecting lines of non-adjacent vertices (in the figure AC = e and BD = f) are the diagonals of the quadrilateral.

There are α and γ and β and δ opposite angles;

α and β , β and γ , γ and δ and δ and α are adjacent angles.

The perimeter u of a quadrilateral ABCD is the sum of the side lengths:

u = a + b + c + d

The sum of the interior angles of a quadrilateral ABCD is 360°:

α +β +γ +δ=360°.

Proof:

The quadrilateral ABCD is divided by a diagonal into two triangles whose sum of angles is 180° each:

Δ ABC: α1+β+γ1=180°

Δ ACD: α2+γ2+δ=180°

With α1+α2=α and γ1+γ2=γ then in the quadrilateral ABCD holds:

(α1+α2)+β+(γ1+γ2)+δ=2⋅180°

α+β+γ+δ=360° (w. z. b. w. )

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