Are diagonals equal in a regular polygon?

Regular polygons A triangle has no diagonals. A square has two diagonals of equal length, which intersect at the center of the square. The ratio of a diagonal to a side is. A regular pentagon has five diagonals all of the same length.

Do diagonals of a quadrilateral always bisect each other?

If a quadrilateral is a parallelogram, then its diagonals bisect each other. If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

For which of the following diagonals do not bisect each other?

Answer: A kite as they cross at right angles but they don’t bisect each other.

Are diagonals of a regular pentagon equal?

We now know that each diagonal is parallel to one of the sides. So if we draw two diagonals, they make with their parallel side a parallelogram. But since the sides of the regular pentagon are equal, the parallelogram is a rhombus.

Which quadrilateral does not always have diagonals that bisect each other?

If diagonals bisect each other, opposite sides of quadrilateral are equal and it would be a parallelogram. But then diagonals may not be congruent. If they are congruent, then it must be a rectangle. As diagonals are not perpendicular, it cannot be a square or rhombus (latter does not have congruent diagonals).

What must be proven to prove that the diagonals bisect each other?

Theorem: The diagonals of a parallelogram bisect each other. Proof: Given ABCD, let the diagonals AC and BD intersect at E, we must prove that AE ∼ = CE and BE ∼ = DE. The converse is also true: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

How many diagonals does a regular polygon?

So, total diagonals contained within an 11-sided polygon = 55 -11 which is equal to 44. Formula Method: According to the formula, the number of diagonals equals n (n-3)/ 2. So, 11-sided polygon will contain 11(11-3)/2 = 44 diagonals….Solved Examples.