How do you prove that a quadrilateral with vertices is a rectangle?

How do you prove that a quadrilateral with vertices is a rectangle?

There are a few ways to prove a quadrilateral is a rectangle. Here are three of the easiest ways: 1) Show all angles are 90°; 2) Show that one pair of sides is parallel and that two opposite angles are 90°; 3) Show the diagonals bisect each other and are of equal length.

What is the vertices of a parallelogram?

4
Parallelogram/Number of vertices

How do you verify a parallelogram?

Well, we must show one of the six basic properties of parallelograms to be true!

1. Both pairs of opposite sides are parallel.
2. Both pairs of opposite sides are congruent.
3. Both pairs of opposite angles are congruent.
4. Diagonals bisect each other.
5. One angle is supplementary to both consecutive angles (same-side interior)

What makes a quadrilateral a parallelogram?

A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel . Opposite sides are congruent; Adjacent angles are supplementary; The diagonals bisect each other.

Can you prove that the quadrilateral is a parallelogram based on the given information?

If both pairs of opposite angles of a quadrilateral are congruent, then it’s a parallelogram (converse of a property). If the diagonals of a quadrilateral bisect each other, then it’s a parallelogram (converse of a property).

How is a quadrilateral a rectangle?

A rectangle is a quadrilateral with four right angles. Thus, all the angles in a rectangle are equal (360°/4 = 90°). Moreover, the opposite sides of a rectangle are parallel and equal, and diagonals bisect each other.

Is the quadrilateral ABCD a parallelogram?

Prove: Quadrilateral ABCD is a parallelogram. Ex: Determine if each of the following is a parallelogram and give a reason. a. Given: a < b

How do you prove a quadrilateral is a rhombus?

Proving a quadrilateral is a rhombus: A quadrilateral is a rhombus if 1. or 2. or 3. Ex: Quadrilateral RHOM has vertices R(2, 4), H(–5, 5), O(0, 0) and M(7, –1). Prove using coordinate geometry that RHOM is a rhombus. Square Definition: A square is a quadrilateral Note: A square is a

How do you prove a parallelogram is a rectangle?

Theorem: A parallelogram with one right angle is a rectangle. Given: Parallelogram ABCD, (A is a right angle Prove: ABCD is a rectangle Theorem: A parallelogram with congruent diagonals is a rectangle. Given: Parallelogram ABCD,

How do you prove ABCD is a rectangle?

Prove: ABCD is a rectangle Theorem: A parallelogram with congruent diagonals is a rectangle. Given: Parallelogram ABCD, Prove: ABCD is a rectangle Proving a quadrilateral is a rectangle: A quadrilateral is a rectangle if 1. or 2. or 3. Ex: Determine if each of the following is a rectangle and give a reason.