If the measure if one angle of a parallelogram is 90 degrees, what is the probability that the parallelogram is a rectangle?

1 answer:

8 0

The probability is 100%.

Definition of rectangle:
A rectangle is a parallelogram with one right angle.

Remember that in math, "one right angle" means "at least one right angle."
If a parallelogram has one right angle, it must be a rectangle, and all angles are right angles.

This is why.
There are different ways to show this.
Here is one of them.
Opposite angles of a parallelogram are congruent.
If one angle measures 90 degrees, the opposite angle must also measure 90 degrees. You already have two right angles.
The sum of the measures of the angles of a quadrilateral is 360.
Two angles are right angles which add to 180 deg.
360 deg - 180 deg = 180 deg.
The other two angles have measures that also add up to 180 deg.
Since the other pair of opposite angles is also congruent, then both angles must measure 90 deg.
Therefore, if a parallelogram has one right angle, it must have 4 right angles, and it is a rectangle.

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\text {Length of AB}= \sqrt{(4-0)^2 + (4-2)^2} = \sqrt{16 + 4} = \sqrt{20} = 4.47 \text{ units}$
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