Are the diagonals of a rhombus always congruent?

The diagonals of a parallelogram are sometimes congruent. The diagonals of a rhombus are always perpendicular. The consecutive angles of a parallelogram are never complementary.

What type of rhombus has congruent diagonals?

Quadrilaterals

Can diagonals be congruent?

Properties of a Rectangle The diagonals are congruent and bisect each other (divide each other equally). Opposite angles formed at the point where diagonals meet are congruent. A rectangle is a special type of parallelogram whose angles are right.

What are the 4 properties of a rhombus?

A rhombus is a quadrilateral which has the following four properties:

• Opposite angles are equal.
• All sides are equal and, opposite sides are parallel to each other.
• Diagonals bisect each other perpendicularly.
• Sum of any two adjacent angles is 180°

How do you prove lines are congruent?

If two parallel lines are cut by a transversal, then corresponding angles are congruent. If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

How do you know if diagonals are congruent?

The first way to prove that the diagonals of a rectangle are congruent is to show that triangle ABC is congruent to triangle DCB. Since ABCD is a rectangle, it is also a parallelogram. Since ABCD is a parallelogram, segment AB ≅ segment DC because opposite sides of a parallelogram are congruent.

What are the 5 properties of rhombus?

Properties of Rhombus

• All sides of the rhombus are equal.
• The opposite sides of a rhombus are parallel.
• Opposite angles of a rhombus are equal.
• In a rhombus, diagonals bisect each other at right angles.
• Diagonals bisect the angles of a rhombus.
• The sum of two adjacent angles is equal to 180 degrees.

Does a rhombus have a 90 angle?

Explanation: As a parallelogram, rhombus has a sum of two interior angles that share a side equal to 180∘ . Therefore, only if all angles are equal, they all are equal to 90∘ . That equality of all angles makes a square out of rhombus.

Are angles of rhombus 90?

In Euclidean geometry, a rhombus is a special type of quadrilateral that appears as a parallelogram whose diagonals intersect each other at right angles, i.e., 90 degrees. As the shape of a rhombus is just like that of a diamond, it is also known as diamond.

Can 2 lines be congruent?

Theorem 6.5: Two line segments are congruent if and only if they have the same length.

How are the two diagonals of a rhombus related?

A rhombus has four sides and its two diagonals bisect each other at right angles. If all the angles of a rhombus are 90 degrees, a rhombus is a square or a rectangle. Since all the sides of the rhombus are congruent, and the opposite angles are parallel to each other, the area of the rhombus is given as:

How are the sides of a rhombus congruent?

There are several formulas for the rhombus that have to do with its: All 4 sides are congruent. Diagonals bisect vertex angles. Diagonals are perpendicular. Is a Square a Rhombus? Yes, a square is a rhombus A square must have 4 congruent sides. Every rhombus has 4 congruent sides so every single square is also a rhombus.

How are the diagonals of a rectangle congruent?

A rectangle has two diagonals as it has four sides. Like a square, the diagonals of a rectangle are congruent to each other and bisect each other. If a diagonal bisects a rectangle, two congruent right triangles are obtained.

Is the shape below a rhombus or a parallelogram?

If not, classify the shape. The shape below is not a rhombus because its diagonals are not perpendicular. However, since opposite sides are congruent and parallel, and the diagonals bisect each other. The shape below is a parallelogram. The diagonals bisect the vertex angles of a rhombus. A proof of this property of the diagonals