Table of Contents
- 1 Are the diagonals of a quadrilateral always equal?
- 2 Why a quadrilateral is a parallelogram if the diagonals bisect each other?
- 3 Which quadrilateral have diagonals that are equal?
- 4 What happens if the diagonals of a quadrilateral bisect each other?
- 5 What can the diagonals of a quadrilateral determine about its shape?
- 6 Are the diagonals of a parallelogram of equal length?
Are the diagonals of a quadrilateral always equal?
FALSE , Diagonals of parallelogram are not necessarily equal. A quadrilateral can only be called a parallelogram if both pairs of its opposite sides are equal. If all angles are equal, then it means its opposite angles are also equal which is a condition for a quadrilateral to be called parallelogram.
Why a quadrilateral is a parallelogram if the diagonals bisect each other?
Theorem: The diagonals of a parallelogram bisect each other. Proof: Given ABCD, let the diagonals AC and BD intersect at E, we must prove that AE ∼ = CE and BE ∼ = DE. The converse is also true: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Is if the diagonals of a quadrilateral bisect each other then the quadrilateral is a square?
A quadrilateral that has diagonals that bisect and are perpendicular must be a square. A kite with congruent diagonals is a square.
In which of the following Quadrilaterals diagonals are equal?
In a parallelogram, opposite sides are equal, opposite angles are equal and diagonals bisect each other. In a rhombus diagonals intersect at right angles. In a rectangle diagonals are equal.
Which quadrilateral have diagonals that are equal?
A parallelogram with one right angle is a rectangle. A quadrilateral whose diagonals are equal and bisect each other is a rectangle.
What happens if the diagonals of a quadrilateral bisect each other?
The converse is also true: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. Theorem: Opposite angles of a parallelogram are congruent to each other. A rhombus is a parallelogram with all four sides congruent to each other.
For which of the following quadrilateral diagonals bisect each other?
Solution: (i) If diagonals of a quadrilateral bisect each other then it is a rhombus, parallelogram, rectangle or square. (ii) If diagonals of a quadrilateral are perpendicular bisector of each other, then it is a rhombus or square. (iii) If diagonals are equal, then it is a square or rectangle.
How do you prove that a quadrilateral is a parallelogram?
Proof: Since the diagonals bisect each other, we already know (from Theorem 1) that it is a parallelogram, so all we need to prove is that the angles at the vertices are right angles. Again let the quadrilateral be ABCD with diagonals AC and BD intersecting at P . Since the diagonals bisect each other,…
What can the diagonals of a quadrilateral determine about its shape?
The diagonals of a quadrilateral can determine whether it is a parallelogram, a rectangle, a rhombus, etc.. We will list and prove the main theorems here.
Are the diagonals of a parallelogram of equal length?
The diagonals of a parallelogram are not of equal length. They bisect with each other at the point of intersection with equal sides across the point of intersection. This can be proved using the ASA criterion as well. When we divide the parallelogram through two diagonals, we see that four triangles are formed.
How do you prove that a parallelogram is a rhombus?
Theorem 3: If the diagonals of a quadrilateral bisect each other and are perpendicular then the quadrilateral is a rhombus. Theorem 6: If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.