How do you prove that if the diagonals of a parallelogram are congruent then the parallelogram is a rectangle?

If a parallelogram is a rectangle, then its diagonals are congruent. If one angle of a parallelogram is a right angle, then the parallelogram is a rectangle. If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

Is the length of the diagonals of a parallelogram are equal then which of this condition is always true?

If the diagonals of a parallelogram are equal in length, then prove that the parallelogram is a rectangle.

Is the diagonals of a parallelogram are equal?

Are the Diagonals of a Parallelogram Equal? The diagonals of a parallelogram are NOT equal. The opposite sides and opposite angles of a parallelogram are equal.

How do you prove that the diagonals of a parallelogram are congruent?

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.

How do you prove a parallelogram?

There are five ways to prove that a quadrilateral is a parallelogram:

1. Prove that both pairs of opposite sides are congruent.
2. Prove that both pairs of opposite sides are parallel.
3. Prove that one pair of opposite sides is both congruent and parallel.
4. Prove that the diagonals of the quadrilateral bisect each other.

How do you prove diagonals bisect each other with coordinates?

To prove that the diagonals bisect each other, we have to show that they have the same midpoint; that is, we have to show that their midpoints have the same coordinates. Since the midpoints of the diagonals have the same coordinates, the theorem is proved.

How do you prove that the diagonals of a parallelogram are equal?

Solution: Given: The diagonals of a parallelogram are equal. To show that a given parallelogram is a rectangle, we have to prove that one of its interior angles is 90° and this can be done by the concept of congruent triangles.

Which method can be used to prove if a parallelogram is a rectangle?

If a parallelogram is known to have one right angle, then repeated use of co-interior angles proves that all its angles are right angles. If one angle of a parallelogram is a right angle, then it is a rectangle.

How do you know if diagonals are equal?

The diagonals of a rectangle are equal. Let ABCD be a rectangle. We prove that AC = BD. Hence AC = DB (matching sides of congruent triangles)….

• The opposite angles of a parallelogram are equal.
• The opposite sides of a parallelogram are equal.
• The diagonals of a parallelogram bisect each other.