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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.
What statement about the squares must be true?
The statement that must be true about squares is that all squares are rectangles, but not all rectangles are squares. This is because squares have all sides equal in length and each angle measuring 90 degrees, which satisfies the definition of a rectangle. Additionally, the diagonals of a square are equal in length and bisect each other at right angles, reinforcing its unique properties among quadrilaterals.
What quadrilaterals must have all four sides of the equal length?
A quadrilateral with all four sides of equal length is known as a rhombus. Additionally, if the angles of the rhombus are all right angles, it becomes a square, which is a specific type of rhombus. Therefore, both rhombuses and squares must have all four sides of equal length.
What statements must be true if WXYZ is a square?
If WXYZ is a square, then all four sides are equal in length, meaning WX = XY = YZ = ZW. Additionally, each angle must measure 90 degrees, ensuring that the corners are right angles. The diagonals WX and YZ must also be equal in length and bisect each other at right angles. Finally, the diagonals should intersect at the midpoint of each diagonal.
Why is a square a rhombus but a rhombus is not a square?
Both are quadrilaterals with all sides of equal length. All four vertices of a square must be right angles whereas a rhombus has two pairs of equal angles.
Which quadrilaterals must have diagonals of equal length?
Rectangle and Isosceles Trapezoid
Which quadrilaterals must have perpendicular diagonals?
A square, a rhombus and a kite are all 4 sided quadrilaterals that have perpendicular diagonals.
The diagonals of a parallelogram must be what?
The diagonals of a parallelogram are congruent (equal in length) and bisect each other.
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.
Is a square like a rectangle?
A square has four equal length sides, a rectangle is a four sided shape with potentially different length sides --------------------- A rectangle can have sides of at most two different lengths and opposite sides must be equal. Also, both have four right angles, both have diagonals of equal length that bisect one another. Both (by virtue of being right angled) are cyclic quadrilaterals.
What statement about the squares must be true?
The statement that must be true about squares is that all squares are rectangles, but not all rectangles are squares. This is because squares have all sides equal in length and each angle measuring 90 degrees, which satisfies the definition of a rectangle. Additionally, the diagonals of a square are equal in length and bisect each other at right angles, reinforcing its unique properties among quadrilaterals.
Is a quadrilateral always a kite?
No, all quadrilaterals are trapeziums. I kite must have 2 pairs of adjacent sides equal in length.
Is CZ is a square which statements must be true?
To determine if CZ is a square, the following statements must be true: All four sides of CZ must be equal in length. All four angles of CZ must be right angles (90 degrees). The diagonals of CZ must be equal in length and bisect each other at right angles.
What statements must be true if WXYZ is a square?
If WXYZ is a square, then all four sides are equal in length, meaning WX = XY = YZ = ZW. Additionally, each angle must measure 90 degrees, ensuring that the corners are right angles. The diagonals WX and YZ must also be equal in length and bisect each other at right angles. Finally, the diagonals should intersect at the midpoint of each diagonal.
How many regular quadrilaterals are there?
There is only one regular quadrilateral, the square. A regular polygon must have equal sides and equal angles, and in the case of quadrilaterals that is a square.
Why is a square a rhombus but a rhombus is not a square?
Both are quadrilaterals with all sides of equal length. All four vertices of a square must be right angles whereas a rhombus has two pairs of equal angles.
Why do the diagonals of a rhombus not have to be the same length?
The sides of a rhombus must all be the same length, but the angles do not need to be the same. The result is a diamond shape where the diagonals can be two different lengths.
