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What is the parallelogram theorem?

Joe Ford

What is the parallelogram theorem?

Theorem 1: In a parallelogram, the opposite sides are of equal length. Theorem 2: If the opposite sides in a quadrilateral are the same length, then the figure is a parallelogram. Theorem 3: A quadrilateral is a parallelogram if and only if the diagonals bisect each other.

What is the key property of a parallelogram?

The properties of a parallelogram are as follows: The opposite sides are parallel and congruent. The opposite angles are congruent. The consecutive angles are supplementary.

What are 3 of 8 properties of a parallelogram?

You’ll know that your quadrilateral is a parallelogram if it has these properties of parallelograms:

  • The opposite sides are parallel.
  • The opposite sides are congruent.
  • The opposite angles are congruent.
  • Consecutive angles are supplementary (add up to 180-degrees).
  • The diagonals bisect each other.

What are the 7 properties of parallelogram?

Properties of parallelograms

  • Opposite sides are congruent (AB = DC).
  • Opposite angels are congruent (D = B).
  • Consecutive angles are supplementary (A + D = 180°).
  • If one angle is right, then all angles are right.
  • The diagonals of a parallelogram bisect each other.
  • Each diagonal of a parallelogram separates it into two congruent triangles.

Are the diagonals of a parallelogram equal?

Are the Diagonals of a Parallelogram Equal? The diagonals of a parallelogram are equal. The opposite sides and opposite angles of a parallelogram are equal. And these opposite sides and angles make up for two congruent triangles, with the two diagonals being the sides of these two congruent triangles.

What are supplementary angles in a parallelogram?

A Parallelogram is a flat shape with opposite sides parallel and equal in length. Angles “a” and “b” add up to 180°, so they are supplementary angles.

Are Consecutive angles supplementary in a parallelogram?

PARALLELOGRAMS (rectangles, squares, and rhombi): 1) Opposite sides of a parallelogram are congruent. 2) Opposite angles of a parallelogram are congruent. 3) Consecutive angles in a parallelogram are supplementary.

Is a parallelogram always a quadrilateral?

All parallelograms are quadrilaterals, so if it is a parallelogram, it is also a quadrilateral. The correct answer is that all trapezoids are quadrilaterals.

What parallelogram is not a rhombus?

All rhombuses are parallelograms, but not all parallelograms are rhombuses. All squares are rhombuses, but not all rhombuses are squares. The opposite interior angles of rhombuses are congruent. Diagonals of a rhombus always bisect each other at right angles.

Can a square be classified as a rhombus?

Since a square has 4 right angles, it can also be classified as a rectangle. Since a square has 4 sides of equal length, it can also be classified as a rhombus.

Can a square be a parallelogram?

A square is a parallelogram. Squares are quadrilaterals with 4 congruent sides and 4 right angles, and they also have two sets of parallel sides. Parallelograms are quadrilaterals with two sets of parallel sides. Since squares must be quadrilaterals with two sets of parallel sides, then all squares are parallelograms.

What is the difference between a square rectangle rhombus and a parallelogram?

A parallelogram is a quadrilateral with two pairs of parallel opposite sides. A rhombus is a parallelogram with equal adjacent sides. A square is a rhombus with four equal internal angles. A rectangle is a parallelogram with four equal internal angles.

Why diagonals of rhombus are not equal?

Every rhombus has two diagonals connecting pairs of opposite vertices, and two pairs of parallel sides. Opposite angles of a rhombus have equal measure. The two diagonals of a rhombus are perpendicular; that is, a rhombus is an orthodiagonal quadrilateral. Its diagonals bisect opposite angles.

Are all diagonals of a rhombus equal?

No the diagonals of a rhombus are not always equal. When the diagonals of a rhombus are equal it is called a square. A square is a special kind of rhombus where all four angles are 90 degrees which makes both diagonals the same (length of the side multiplied by the square root of 2).

What is difference between rhombus and parallelogram?

Mention the key difference between the rhombus and parallelogram. In a rhombus, all the four sides are equal and the diagonals intersect at 90 degrees, whereas in a parallelogram, the opposite sides are equal and the diagonals bisect each other.

Are the diagonals of a kite equal?

Every kite is orthodiagonal, meaning that its two diagonals are at right angles to each other. The two interior angles of a kite that are on opposite sides of the symmetry axis are equal.