What is it called when a parallelogram has perpendicular diagonals?

‘If the diagonals of a parallelogram are perpendicular, then it is a rhombus. ‘

How do you prove that the diagonals of a parallelogram are perpendicular?

Show that the diagonals of a parallelogram are perpendicular if and only if it is a rhombus, i.e., its four sides have equal lengths. (A + B) · (A – B) = A · A – B · B. Therefore, (A + B) · (A – B)=0 ⇔ A · A = B · B.

What is perpendicular in a parallelogram?

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.

Which of them have their diagonals perpendicular to each other?

Answer: Rhombus; square.

Which parallelogram has congruent and perpendicular diagonals?

We know a square is a parallelogram with congruent sides and congruent angles, and has diagonals that are congruent and perpendicular.

How do you prove that two lines are perpendicular in a parallelogram?

If the two lines intersect at a point, the vertical angles formed are congruent. The intersecting lines either form a pair of acute angles and a pair of obtuse angles, or the intersecting lines form four right angles. When the lines meet to form four right angles, the lines are perpendicular.

For which of the following quadrilateral diagonals are perpendicular to each other a parallelogram B kite C Trapezium D rectangle?

In kite, diagonals are perpendicular to each other is as shown in the figure below. A kite is a quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.

For which of the following quadrilaterals diagonals are perpendicular to each other 1 point parallelogram trapezium rectangle kite?

Which quadrilateral does not have diagonals that are perpendicular?

Rectangle is the quadrilateral, which has diagonals that are congruent and bisect but are not perpendicular.

How do you know if a diagonal is perpendicular?

Proof that the diagonals of a rhombus are perpendicular Corresponding parts of congruent triangles are congruent, so all 4 angles (the ones in the middle) are congruent. This leads to the fact that they are all equal to 90 degrees, and the diagonals are perpendicular to each other.