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

The opposite sides of a parallelogram are equal. ABCD is a parallelogram. To prove that AB = CD and AD = BC….A quadrilateral is a parallelogram if:

1. its opposite angles are equal, or.
2. its opposite sides are equal, or.
3. one pair of opposite sides are equal and parallel, or.
4. its diagonals bisect each other.

How do you prove 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.

How do you prove a parallelogram is a rhombus?

If two consecutive sides of a parallelogram are congruent, then it’s a rhombus (neither the reverse of the definition nor the converse of a property). If either diagonal of a parallelogram bisects two angles, then it’s a rhombus (neither the reverse of the definition nor the converse of a property).

What properties of parallelograms can be used to prove parallelogram theorems select all that apply?

There are six important properties of parallelograms to know:

• Opposite sides are congruent (AB = DC).
• Opposite angels are congruent (D = B).
• Consecutive angles are supplementary (A + D = 180°).
• If one angle is right, then all angles are right.
• The diagonals of a parallelogram bisect each other.

What is congruent in a parallelogram?

A parallelogram also has the following properties: Opposite angles are congruent; Opposite sides are congruent; Adjacent angles are supplementary; The diagonals bisect each other.

What are the theorems of parallelogram?

Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

How do you prove a parallelogram in coordinate geometry?

Therefore, one way to prove it is a parallelogram is to verify that the opposite sides are parallel. From algebra, remember that two lines are parallel if they have the same slope. Find the slope of each side and label it on the picture. The slopes of the opposite sides are equal.

What are parallelograms properties?

Properties of Parallelogram The opposite sides are parallel and congruent. The opposite angles are congruent. The consecutive angles are supplementary. If any one of the angles is a right angle, then all the other angles will be at right angle. The two diagonals bisect each other.