Proving that a Quadrilateral with One Right Angle is a Parallelogram: Understanding the Relationship Between Opposite Sides

A quadrilateral with one right angle is a parallelogram

To prove that a quadrilateral with one right angle is a parallelogram, we need to show that its opposite sides are parallel

To prove that a quadrilateral with one right angle is a parallelogram, we need to show that its opposite sides are parallel.

Let’s consider a quadrilateral ABCD with one right angle at vertex D.

First, draw diagonal AC between vertices A and C.

Now, let’s look at the triangle ABC. Since angle D is a right angle, angle BAC is also a right angle (as the sum of angles in a triangle is 180 degrees). So, in triangle ABC, we have two angles BAC and ACB which are right angles.

Since the sum of angles in a triangle is 180 degrees, this means that angle ABC is also a right angle.

Now, let’s look at the quadrilateral ABCD again. We have opposite angles DAB and BCD that are both right angles. By definition, a quadrilateral with opposite right angles is a parallelogram.

Therefore, we can conclude that a quadrilateral with one right angle is indeed a parallelogram because its opposite sides are parallel.

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