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Quadrilateral, general

The vertices of a (convex) quadrilateral are usually designated with capital letters - https://domyhomework.club (e.g. A, B, C and D), the sides with small letters a, b, c and d, and the (interior) angles with α, β, γ and δ in the mathematical positive sense of circulation, 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 - https://domyhomework.club/math-homework/ . 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. )

Rectangle

A parallelogram with a right angle is a rectangle - geometry homework help . Consequently, the following is true for the rectangle:

- The opposite sides are of equal length and parallel to each other.

- Adjacent sides are at right angles to each other.

- All four interior angles are equal. They are 90°.

- The diagonals are of equal length and bisect each other.

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