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What quadrilateral has the diagonals of a perpendicular bisectors of equal length?
A square.
Are the diagonals of a square equal and perpindicular besides bisecting each other?
Yes, the diagonals of a square are congruent (equal in length) and are perpendicular.
What is a shape with four sides and perpendicular diagonals?
A shape with four sides and perpendicular diagonals is called a rhombus. In a rhombus, all sides are of equal length, and the diagonals bisect each other at right angles. Additionally, the diagonals are not necessarily of equal length, which distinguishes a rhombus from a square.
How do you prove that the diagonals of a square are equal and perpendicular to each other?
To prove that the diagonals of a square are equal and perpendicular, start by noting that a square has four equal sides and four right angles. By using the distance formula, calculate the lengths of the diagonals; since both diagonals connect opposite vertices, they will have the same length, confirming they are equal. To show they are perpendicular, observe that the slopes of the diagonals are negative reciprocals of each other, as they intersect at right angles, demonstrating that the diagonals are perpendicular. Thus, the properties of the square ensure that both conditions are satisfied.
Is a square a parallelogram with diagonals congruent and perpendicular?
Yes, a square is a special type of parallelogram. By definition, a parallelogram has opposite sides that are equal and parallel, and in a square, all four sides are equal. Additionally, a square has diagonals that are both congruent (equal in length) and perpendicular (intersecting at right angles), which further distinguishes it from other types of parallelograms.
What quadrilateral has the diagonals of a perpendicular bisectors of equal length?
A square.
Are the diagonals of a square equal and perpindicular besides bisecting each other?
Yes, the diagonals of a square are congruent (equal in length) and are perpendicular.
Are the diagonals of a rhombus perpendicular and bisect each other?
Yes, they are perpendicular and intersect at their midpoints. The difference between diagonals in a rhombus as opposed to a rectangle or square is that the diagonals are not of equal length.
What is a shape with four sides and perpendicular diagonals?
A shape with four sides and perpendicular diagonals is called a rhombus. In a rhombus, all sides are of equal length, and the diagonals bisect each other at right angles. Additionally, the diagonals are not necessarily of equal length, which distinguishes a rhombus from a square.
How do you prove that the diagonals of a square are equal and perpendicular to each other?
To prove that the diagonals of a square are equal and perpendicular, start by noting that a square has four equal sides and four right angles. By using the distance formula, calculate the lengths of the diagonals; since both diagonals connect opposite vertices, they will have the same length, confirming they are equal. To show they are perpendicular, observe that the slopes of the diagonals are negative reciprocals of each other, as they intersect at right angles, demonstrating that the diagonals are perpendicular. Thus, the properties of the square ensure that both conditions are satisfied.
A quadrilateral with equal diagonals that are also perpendicular?
A square
Is a square a parallelogram with diagonals congruent and perpendicular?
Yes, a square is a special type of parallelogram. By definition, a parallelogram has opposite sides that are equal and parallel, and in a square, all four sides are equal. Additionally, a square has diagonals that are both congruent (equal in length) and perpendicular (intersecting at right angles), which further distinguishes it from other types of parallelograms.
What type of figure must a quadrilateral be if its diagonals are perpendicular bisectors of each other and are congruent?
It is a square because its diagonals are equal in length and they bisect each other at right angles which is 90 degrees The diagonals of a rhombus are not equal in length but they meet at right angles.
Diagonals of equal length?
square
How does a square differ from a rhombus?
A square is a rhombus with all angles 90o. When the angles of a rhombus are not all 90o, it differs from the square in this respect, and the diagonals are not of equal length unlike those of a square. A rhombus is like a square in that all its sides are equal in length, opposite sides are parallel and the diagonals are perpendicular and bisect each other.
The diagonals of a square are equal in length?
Yes.
What shape has 4 equal sides and equal length diagonals?
a square
