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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 ...
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.
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.
Equidiagonal quadrilateral: the diagonals are of equal length. Bisect-diagonal quadrilateral: one diagonal bisects the other into equal lengths. Every dart and kite is bisect-diagonal. When both diagonals bisect another, it's a parallelogram. Ex-tangential quadrilateral: the four extensions of the sides are tangent to an excircle.
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.
Hints show the letters of a theme word. If there is already an active hint on the board, a hint will show that word’s letter order. Related: 300 Trivia Questions and Answers to Jumpstart Your ...
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°.
Hints show the letters of a theme word. If there is already an active hint on the board, a hint will show that word’s letter order. Related: 300 Trivia Questions and Answers to Jumpstart Your ...