Study guides

☆☆

Q: If a parallelogram has one right angle then all of its angles must be right?

Write your answer...

Submit

Still have questions?

Continue Learning about Geometry

Definition I was taught: "A rectangle is a parallelogram with one right angle" Sounds weird but when you think it out, having one right angle in a parallelogram means the other three must be right as well.

No because it could be a right angled trapezoid. A rectangle must have four right angles. Yes, a parallelogram with a right angle is always a rectangle. In fact, in my geometry book, some 55 years ago such was the definition of rectangle. A parallelogram with one right angle will always have four right angles. The right angled trapezoids that are not rectangles are not parallelograms.

FALSE because a rectangle has 4 right angles.

A parallelogram with at least one right angle

square or a rhombus

Related questions

No parallelogram can have only one right angle. The consecutive angles of a parallelogram must be supplementary, meaning they must add up to 180. 180-90=90, so all the angles must be right angles.

A parallelogram cannot have just one right angle. If it has one, all four of its angles must be right angles and so it must be a rectangle (or, as a special case, a square).

Every parallelogram has 4 sides.If it has 4 right angles, then it's a rectangle.(Actually, a parallelogram with one right angle must be a rectangle.)

Definition I was taught: "A rectangle is a parallelogram with one right angle" Sounds weird but when you think it out, having one right angle in a parallelogram means the other three must be right as well.

No because it could be a right angled trapezoid. A rectangle must have four right angles. Yes, a parallelogram with a right angle is always a rectangle. In fact, in my geometry book, some 55 years ago such was the definition of rectangle. A parallelogram with one right angle will always have four right angles. The right angled trapezoids that are not rectangles are not parallelograms.

FALSE because a rectangle has 4 right angles.

A rectangle, possibly a square. Can you see why a parallelogram must be a rectangle if any one of its angles is right?

No, a paralleogram that has even one right angle must have all right angles in order to keep the opposite sides parallel. So, a parallelogram will have either no right angles (in which case it will always have 2 acute angles and two obtuse angles) or it will have 4 right angles (in which case it will be called a square or a rectangle, and will obviously have no acute or obtuse angles).

It is not a requirement that any of the angles are right angles (90 degrees), to qualify as a parallelogram.

Not all parallelograms are rectangles. A parallelogram is a shape with two parallel sides. Sometimes a parallelogram is a rhombus, trapezoid or a square.

4 right angles

One angle must be 90o, which is the right angle. The sum of the other two angles must equal 90o.

People also asked