Do equal diagonals bisect each other?

A rectangle is a quadrilateral in which all angles are right angles. A rectangle is a parallelogram, so its opposite sides are equal. The diagonals of a rectangle are equal and bisect each other.

In which quadrilateral both diagonals are equal and bisect each other?

Rhombus
Rhombus: In rhombus, all sides are equal and diagonals are perpendicular bisectors of each other. Also, each diagonal is the angle bisector of both the opposite angles.

Is it true that if the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallelogram?

That is, if both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Theorem: The diagonals of a parallelogram bisect each other. The converse is also true: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

In which quadrilateral diagonals do not bisect each other?

Trapezium and Parallelogram are two quadrilateral whose diagonals do not bisect each other at right angles.

In which of the following the diagonals bisect each other quadrilateral rhombus Trapezium concave quadrilateral?

ABCD is a square in which diagonals AC and BD bisect each other in other words it divides into two equal parts.

Which quadrilateral has two pairs of adjacent sides equal and diagonals do not bisect each other?

Rhombus, is a quadrilaterals has two pairs of adjacent sides equal and diagonals intersecting at right angles. A rhombus is a a parallelogram and a quadrilateral whose opposite sides are parallel and opposite angles are equal. The opposite angles of a rhombus are equal to each other.

How do you prove that diagonals of a parallelogram bisect each other?

Expert Answer:

1. ABCD is a parallelogram, diagonals AC and BD intersect at O.
2. In triangles AOD and COB,
3. DAO = BCO (alternate interior angles)
4. AD = CB.
5. ADO = CBO (alternate interior angles)
6. AOD COB (ASA)
7. Hence, AO = CO and OD = OB (c.p.c.t)
8. Thus, the diagonals of a parallelogram bisect each other.

How do you prove that the diagonals of a rectangle bisect each other?

1 Answer

1. AC and OB are diagonals. In the figure let the intersecting point of OB and AC be P. To show that diagonals bisect each other we have to prove that OP = PB.
2. OP = OB. Similarly we can prove that PC = PA. Thus diagonals bisect each other in a rectangle .
3. ∴ The diagonals of a rectangle bisects each other and equal .

What quadrilateral has diagonals bisect opposite angles?

rhombus
If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles. If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus.

Which of the following diagonals bisect each other?

Answer : In a square the diagonals bisect each other because both the opposite side pairs of a square are parallel. But in a trapezium only one pair of opposite pair are parallel. In a kite no opposite pairs are parallel.