## Question: How To Prove A Quadrilateral Is A Rectangle Using Coordinate Geometry?

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.

## How do you prove that 4 points make a rectangle?

(i) Plot the given points in the graph and join the points. (ii) Find the length of all sides. (iii) In a rectangle, the length of opposite sides will be equal. (iv) The rectangle can be divided into two right triangles.

## 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.

## How do you prove a rectangle is a coordinate?

Prove it is a Rectangle

1. – The opposite sides are parallel and congruent. – The diagonals bisect each other.
2. – There are 4 right angles. – The diagonals are congruent.
3. A(0, -3), B(-4, 0), C(2, 8), D(6, 5)
4. – Show that both pairs of opposite sides are congruent. – Show that both pairs of opposite sides are parallel.
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## How do you identify a quadrilateral?

A quadrilateral is a closed figure with four sides and four vertices. A rectangle is a quadrilateral with four right angles. A rhombus is a quadrilateral with four congruent sides. A trapezoid is a quadrilateral with exactly one pair of parallel opposite sides.

## How do you prove a quadrilateral is a square?

Proving that a Quadrilateral is a Square If the quadrilateral is a rectangle with two consecutive sides congruent, then it is a square. If the quadrilateral is a rectangle with perpendicular diagonals, then it is a square. If the quadrilateral is a rhombus one of whose angles is a right angle, then it is a square.

## How do you prove that the points are vertices of a rectangle?

To show: The points are the vertices points of a rectangle. Solution: We know, opposite sides are equal form a rectangle. We find the distance between two points and check any two sides are equal or not.

## How do you prove a quadrilateral is 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.

## How do you prove a cyclic quadrilateral is a rectangle?

Each angle of a rectangle is a right angle. For a cyclic quadrilateral, sum of opposite angles is 180°. => 90° + 90° = 180° ( sum of opposite angles of a rectangle ). Hence, rectangle is a cyclic quadrilateral.

## Is a quadrilateral a rectangle yes or no?

A quadrilateral is any polygon with four sides. A rectangle, by definition, is a polygon with four sides and four right angles. Every rectangle is a quadrilateral because all rectangles must have four sides, which is the definition of a quadrilateral.