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The diagonals bisect each other. One pair of opposite sides is parallel and equal in length. Adjacent angles are supplementary. Each diagonal divides the quadrilateral into two congruent triangles. The sum of the squares of the sides equals the sum of the squares of the diagonals.
AD' is clearly the median, because a parallelogram's diagonals bisect each other, and AD is its reflection about the bisector. third proof. Let ω be the circle with center D passing through B and C, and let O be the circumcenter of ABC. Say lines AB, AC intersect ω at P, Q, respectively. Since ∠ABC = ∠AQP, triangles ABC and AQP are ...
In other words, parallelograms include all rhombi and all rhomboids, and thus also include all rectangles. Rhombus, rhomb: [1] all four sides are of equal length (equilateral). An equivalent condition is that the diagonals perpendicularly bisect each other. Informally: "a pushed-over square" (but strictly including a square, too).
To bisect an angle with straightedge and compass, one draws a circle whose center is the vertex. The circle meets the angle at two points: one on each leg. Using each of these points as a center, draw two circles of the same size. The intersection of the circles (two points) determines a line that is the angle bisector.
All four internal angles of a square are equal (each being 360°/4 = 90°, a right angle). The central angle of a square is equal to 90° (360°/4). The external angle of a square is equal to 90°. The diagonals of a square are equal and bisect each other, meeting at 90°.
Every kite is an orthodiagonal quadrilateral, meaning that its two diagonals are at right angles to each other. Moreover, one of the two diagonals (the symmetry axis) is the perpendicular bisector of the other, and is also the angle bisector of the two angles it meets. [1] Because of its symmetry, the other two angles of the kite must be equal.
The diagonals of an isosceles trapezoid have the same length; that is, every isosceles trapezoid is an equidiagonal quadrilateral. Moreover, the diagonals divide each other in the same proportions. As pictured, the diagonals AC and BD have the same length (AC = BD) and divide each other into segments of the same length (AE = DE and BE = CE).
Using congruent triangles, one can prove that the rhombus is symmetric across each of these diagonals. It follows that any rhombus has the following properties: Opposite angles of a rhombus have equal measure. The two diagonals of a rhombus are perpendicular; that is, a rhombus is an orthodiagonal quadrilateral. Its diagonals bisect opposite ...