# Write a coordinate proof to show that the diagonals of a rectangle are congruent

Tick your answer here Yes, the quadrilateral is a parallelogram because both pairs of opposite sides are congruent. If we can show that the slopes of the opposite sides are the same, then the opposite sides are parallel.

This shows that for any rectangle, the diagonals will be congruent.

Proof: First we will look at only one diagonal. In order to successfully complete a proof, it is important to think of the definition and the construction of a rectangle.

Segment AC is congruent to segment BD. Two of the right triangles have been drawn. In this example, we will show that both pairs of opposite sides are parallel.

Is the quadrilateral a parallelogram?

## Congruent diagonals meaning

Tick your answer here. Then use the distance formula to calculate the length of the segment. In this example, we will show that both pairs of opposite sides are parallel. No, the quadrilateral is not a parallelogram because, even though opposite sides are congruent, we don't know whether they are parallel or not. Is the quadrilateral a parallelogram? Using the sides as hypotenuses, we construct right triangles on the four sides of the quadrilateral. Compare the measured and calculated lengths. If you already know that the shape is a parallelogram, you will only have to show that one of the angles is a right angle and then it would follow that all of the angles are right angles. Based on your side length measurements and calculations can you conclude that the quadrilateral is a parallelogram? Step 2:Prove that the figure is a parallelogram. Consider properties of parallel lines. To do this we need to calculate the slope of each side. Return to the Table of Contents. Then we will look at both diagonals. Click here to investigate this sketch to help with the steps of the proof.

Tick your answer here. Other ways would include showing that the shape has 4 right angles.

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