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Isosceles trapezoid and rectangle
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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.
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.
What is the angle sum rule for all quadrilaterals?
The sum of all (interior) angles must equal 360 degrees
What is the quadrilateral with three equal angles?
With quadrilaterals, if there are three equal angles, then we know that the fourth angle must be equal, so the quadrilateral is a rectangle. * * * * * That is absolute rubbish. You can have a quadrilateral with three angles of 70 degrees and the fourth of 150 degrees. There is no name for such quadrilaterals and the only thing that can be said about them is that they are irregular.
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.
Is a quadrilateral always a kite?
No, all quadrilaterals are trapeziums. I kite must have 2 pairs of adjacent sides equal in length.
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.
Are the diagonals of a trapezoid equal?
Not for all trap. Only for an isosceles trapezoid. Well, for an Isosceles trapezoid, it could be any of the two diagonals! In order to have an isosceles trapezoid with the diagonals equal, the isosceles part MUST be precise and specific.
Is t he two diagonals connecting opposite corners of a rhomboid must always be equal?
This is false for all rhomboids (a distinct parallelogram such that 4 sides are equal, and has non-right angles), since by congruency, a parallelogram can be flipped on its axis (with 2 closer vertices), producing 2 unequal length diagonals.
Why must concave quadrilaterals be irregular?
A regular polygon has all its angles of equal measure, and its sides of equal length. In the case of a quadrilateral, that would mean a square. A concave quadrilateral must have at least one reflex angle and so cannot be a square. So it cannot be regular.
