no
No.
Yes
not all
A trapezoid Trapezoid - 2 congruent diagonals that do not bisect each other. No right angles and has 1 pair of opposite parallel sides.
No, never. A trapezoid may have diagonals of equal length (isosceles trapezoid), but they do not intersect at their midpoints.Draw the diagonals of a trapezoid, for example, an isosceles trapezoid, thereby creating 4 triangles inside the trapezoid. Now assume the diagonals do bisect each other. The congruent corresponding sides of the top and bottom triangles with the included vertical angle would make the triangles congruent by the side-angle-side theorem. But this is a contradiction since the respective bases of the triangles, forming the top and bottom of the trapezoid are, of course, not equal. Therefore, the triangles cannot be congruent. Hence, we have given proof by contradiction that diagonals in a trapezoid cannot bisect each other.
An isosceles trapezoid, or any trapezoid, does not have diagonals that bisect each other.
No.
In an isosceles trapezium (or isosceles trapezoid), the diagonals do not bisect the angles at the vertices where they meet. While the angles at the base are equal, the angles at the top are also equal but not necessarily bisected by the diagonals. The diagonals are equal in length and create two congruent triangles, but they do not divide the angles into equal parts.
Usually they do not, but in an isosceles trapezoid they do.
No, the diagonals of a trapezoid do not necessarily bisect each other. Only in an isosceles trapezoid, where the two non-parallel sides are congruent, will the diagonals bisect each other. In a general trapezoid, the diagonals do not bisect each other.
Yes
not all
yes
In a trapezoid, the diagonals do not generally bisect each other. Unlike parallelograms, where the diagonals always bisect each other, trapezoids have a different geometric property due to their unequal side lengths. The only exception is in an isosceles trapezoid, where the diagonals are congruent but still do not bisect each other at the midpoint.
trapezoid
A trapezoid Trapezoid - 2 congruent diagonals that do not bisect each other. No right angles and has 1 pair of opposite parallel sides.
No, never. A trapezoid may have diagonals of equal length (isosceles trapezoid), but they do not intersect at their midpoints.Draw the diagonals of a trapezoid, for example, an isosceles trapezoid, thereby creating 4 triangles inside the trapezoid. Now assume the diagonals do bisect each other. The congruent corresponding sides of the top and bottom triangles with the included vertical angle would make the triangles congruent by the side-angle-side theorem. But this is a contradiction since the respective bases of the triangles, forming the top and bottom of the trapezoid are, of course, not equal. Therefore, the triangles cannot be congruent. Hence, we have given proof by contradiction that diagonals in a trapezoid cannot bisect each other.