Is a parallelogram with perpendicular diagonals a rectangle?
If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. If a quadrilateral is a rhombus, then it is a parallelogram. If a parallelogram is a rhombus, then its diagonals are perpendicular. If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles.
What is a parallelogram with perpendicular sides?
A Parallelogram with Perpendicular Diagonals is a Rhombus A rhombus is a special kind of parallelogram, in which all the sides are equal. We’ve seen that one of the properties of a rhombus is that its diagonals are perpendicular to each other.
Is a rectangle perpendicular sides?
Like a square, a rectangle has lines that are perpendicular to two other lines. This means it also has four right angles.
Is it true that a parallelogram is a rectangle?
Parallelograms are quadrilaterals with two sets of parallel sides. Since squares must be quadrilaterals with two sets of parallel sides, then all squares are parallelograms. A parallelogram is a rectangle. This is sometimes true.
What parallelogram has perpendicular diagonals?
rhombus
If the diagonals of a parallelogram are perpendicular, it must be a rhombus. Diagonals of a parallelogram bisect the angles. A quadrilateral that has diagonals that bisect and are perpendicular must be a square.
How do you show a parallelogram is a rectangle?
If a parallelogram is known to have one right angle, then repeated use of co-interior angles proves that all its angles are right angles. If one angle of a parallelogram is a right angle, then it is a rectangle.
How many perpendicular sides has a rectangle?
There are 4 right angles, but 2 pairs of perpendicular lines.
How many perpendicular sides are in a parallelogram?
Originally Answered: Does a parallelogram have perpendicular sides? No. A parallelogram is a four sided shape with opposite sides parallel and the same length.
Which shape has perpendicular sides?
Some shapes which have perpendicular lines are: Square. Right-angled triangle. Rectangle.
What parallelogram is not a rectangle?
A rhombus can not be rectangle. In a rhombus all four sides are equal and the diagonals bisect each other. In a rectangle the diagonals bisect each other but not at right angles.
Why is a rectangle always a parallelogram?
Each pair of co-interior angles are supplementary, because two right angles add to a straight angle, so the opposite sides of a rectangle are parallel. This means that a rectangle is a parallelogram, so: Its opposite sides are equal and parallel. Its diagonals bisect each other.
Which quadrilateral is perpendicular?
Quadrilaterals with perpendicular lines have sides that meet at a right angle (90°). Some quadrilaterals also fit into another type. A square is a type of rectangle, and rectangles are also a type of parallelogram.
Does a parallelogram have right angles and perpendicular sides?
A parallelogram is a quadrilateral with opposite sides parallel and congruent. This does not require right angles (perpendicular sides) but it does not exclude right angles either. A parallelogram with right angles (perpendicular) is a rectangle. Originally Answered: Does a parallelogram have perpendicular sides?
Are the diagonals of a parallelogram congruent?
In a parallelogram, diagonals are just bisectors, in a rhombus diagonal are perpendicular bisectors. The diagonals of a rectangle are congruent.
What is the difference between a rectangle and a square?
A rectangle has two pairs of opposite sides parallel, and four right angles. A square has two pairs of parallel sides, four right angles, and all four sides are equal. It is also a rectangle and a parallelogram. A rhombus is defined as a parallelogram with four equal sides.
How do you prove that a parallelogram is a square?
To prove that a parallelogram is a square, we need to prove that it is a rectangleand a rhombus. Theorem:If three or more parallel lines cut ocongruent segments on onetransversal, then they cut ocongruent segments on all other transversals.