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.

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.

How do you prove a parallelogram is a rhombus by vectors?

By symmetry, the diagonals AC and BD bisect each other. So if O is the centre point, BO and DO are the same length. But then if angle AOD is a right angle (and so is angle AOB) then triangles ABO and ADO are congruent by side-angle-side. But then AB = AD and so the parallelogram is a rhombus.

How do you know if a diagonal is perpendicular?

To prove that two lines are perpendicular, when all we have are those two lines, we can use the Linear Pair Perpendicular Theorem – If two straight lines intersect at a point and form a linear pair of equal angles, they are perpendicular.

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.

Which concept can be used to prove that diagonals of a parallelogram bisect each other?

Which concept can be used to prove that the diagonals of a parallelogram bisect each other? A)Congruent Triangles. You just studied 20 terms!

How do you prove that a parallelogram is a square?

The only parallelogram that satisfies that description is a square. Theorem 16.8: If the diagonals of a parallelogram are congruent and perpendicular, the parallelogram is a square….Geometry.

	Statements	Reasons
5.	Parallelogram ABCD is a square	Definition of a square

How do you prove a parallelogram using vectors?

Answer: Let A, B, C, D be the four sides; then if the vectors are oriented as shown in the figure below we have A + B = C + D. Thus two opposite sides are equal and parallel, which shows the figure is a parallelogram.

How do you prove a rhombus?

To prove a quadrilateral is a rhombus, here are three approaches: 1) Show that the shape is a parallelogram with equal length sides; 2) Show that the shape’s diagonals are each others’ perpendicular bisectors; or 3) Show that the shape’s diagonals bisect both pairs of opposite angles.