Are the diagonals of a parallelogram equal? a. The diagonals of a **parallelogram are equal** . The opposite sides and opposite angles of a parallelogram are equal. And these opposite sides and angles form two congruent triangles, **[1]**** ****[2]** in which the two diagonals are the sides of these two congruent triangles. **[3]**** ****[4]**

Also, what are the 5 properties of a parallelogram?

A parallelogram has the following properties:

- Opposite sides are parallel by definition.
**[5]****[6]** - Opposite sides are congruent.
**[7]****[8]** - Opposite angles are congruent.
**[9]****[10]** - The consecutive angles are supplementary.
**[11]****[12]** - Diagonals bisect each other.
**[13]****[14]**

Here, which figure is a parallelogram?

Parallelogram: **A quadrilateral with 2 pairs of parallel sides** .

Also to know which parallelogram has equal diagonals? **[15]**** ****[16]** **A quadrilateral** is a parallelogram, so its opposite sides are equal. **[17]**** ****[18]** The diagonals of a rectangle are equal and bisect each other.**[19]**** ****[20]**

What is the length of the diagonal of a parallelogram?

In a parallelogram, the diagonals bisect each other, so you can set the labeled segments equal to each other and then solve for . DisplayStyle 20 – 3x = 2x – 4 WriteAero 24 = 5x WriteAero 4.8 = x. Then, substitute 4.8 in each labeled segment to get a total of **11.2** for the diagonal length. **[21]**** ****[22]**

**What is the formula for the diagonal of a parallelogram?**

FAQ on Diagonal of Parallelogram Formula

For any parallelogram ABCD, the formula for the lengths of the diagonals is, **p=√x2+y2−2xycosA=√x2+y2+2xycosB p = x 2 + y 2 − 2 xy cos** A = x 2 + y 2 + 2 xy cos B and q=√x2+y2+2xycosA=√x2+y2−2xycosB q = x 2 + y 2 + 2 xy cos A = x 2 + y 2 − 2 xy cos **[23]**** ****[24]**

**Which is not a property of parallelogram?**

If **the four sides do not connect at their end points** , you do not have a closed shape; **[25]**** ****[26]** No parallelogram! If one side is longer than its opposite side, you don’t have parallel sides; **[27]**** ****[28]** No parallelogram! If only one set of opposite sides is congruent, then you don’t have a parallelogram, you have a trapezium. **[29]**** ****[30]**

**What are the three properties of a parallelogram?**

Properties of Parallelogram Explained

- Opposite sides are parallel. ,
**[11]****[31]** - Opposite sides are congruent. ,
**[32]****[33]** - Opposite angles are congruent. ,
**[34]****[35]** - The interior angles (consecutive angles) of an equal-side are supplementary.
**[36]****[37]** - Each diagonal of a parallelogram divides it into two congruent triangles.
**[38]****[39]** - The diagonals of a parallelogram bisect each other.
**[40]****[41]**

**Why is it called a parallelogram?**

Here all sides are equal and all angles are right angles. Diagonals AC and BD are equal. **[42]**** ****[43]** The word ‘parallelogram’ is derived from Middle French ‘parallogram’, Late Latin ‘parallogramum’ and Greek ‘parallelogram’ meaning ” **surrounded by parallel lines”** **[44]**** ****[45]** .

**Which figure is not a parallelogram?**

A simple quadrilateral that has no equal sides is not a parallelogram. A **kite** is not exactly parallel lines. A trapezium and an isosceles trapezium have one pair of opposite sides parallel. The vertex of a concave quadrilateral or arrow does not have parallel sides.**[46]**** ****[47]**** ****[48]**

**Is the triangle a parallelogram?**

**A triangle is a parallelogram** . This is never true.**[1]**** ****[2]** Parallelograms are quadrilaterals with two sets of parallel sides. Since a square must be a quadrilateral with two sets of parallel sides, then all squares are parallelograms.**[3]**** ****[4]**

**Are the diagonals of a rhombus equal?**

a. The diagonals of a **rhombus intersect at equal angles** ,**[5]**** ****[6]** while the diagonals of a rectangle are of equal length.

**Is a parallelogram a rhombus?**

Hence the opposite sides are congruent and the quadrilateral MNOP is a parallelogram. **[7]**** ****[8]** Also, the adjacent sides are congruent, so the parallelogram MNOP a . is

rhombus

. 1.

…

Geometry.

statement | cause | |
---|---|---|

9. | Parallelogram ABCD is a rhombus | definition of rhombus |

**What are the major and minor diagonals of a parallelogram?**

**The diagonal passing through the greater angle is called the minor diagonal** because of its smaller size. **[9]**** ****[10]** The diagonal passing through the smaller angle is called the major diagonal because of its longer shape.

**What is the diagonal formula?**

The formula to calculate the number of diagonals of an n-sided polygon **= n(n-3)/2** where n is the number of sides of the polygon.

**What is the length of the longest diagonal in a parallelogram?**

Answer: The length of the longest diagonal in a parallelogram is **24.86** .**[11]**** ****[12]**

**What is the formula to find the diagonal of a parallelogram?**

FAQ on Diagonal of Parallelogram Formula

For any parallelogram ABCD, the formula for the lengths of the diagonals is, **p=√x2+y2−2xycosA=√x2+y2+2xycosB p** = x 2 + y 2 − 2 xy cos A = x 2 + y 2 + 2 xy cos B and q=√x2+y2+2xycosA=√x2+y2−2xycosB q = x 2 + y 2 + 2 xy cos A = x 2 + y 2 − 2 xy cos

**How do you find the long diagonal of a parallelogram?**

Explanation: In a parallelogram, the diagonals bisect each other, **[13]**** ****[14]** so you can set the labeled segments equal to each other and then solve for . Display Style **20 – 3x = 2x – 4 Right Arrow** 24 = 5x Right Arrow 4.8 = x. Then, substitute 11.2 for each labeled segment to get a total of 4.8 for the diagonal length.**[15]**** ****[16]**

**What is a diagonal?**

In geometry, a diagonal is **the line segment joining two vertices of a polygon or polyhedron** , when those vertices are not on the same edge. Informally, any sloping line is called a diagonal. **[17]**** ****[18]** In matrix algebra, a diagonal of a square matrix is a set of entries extending from one corner to the furthest corner.**[19]****[20]**

**What is the shape of a parallelogram?**

Parallelogram: **A quadrilateral with 2 pairs of parallel sides** .

**Which figure is a quadrilateral but not a parallelogram?**

**A trapezoid** is a quadrilateral that is not a parallelogram because its two sides are not parallel. **[21]****[22]**

**Why are the diagonals of a parallelogram not equal?**

The diagonals of a parallelogram are not equal. If they were, the **figure would be a rectangle** . **[23]**** ****[24]** And if the sides were also equal, the figure would also be a square! Since the adjacent angles in a parallelogram are less and greater, the diagonals split the figure into 2 pairs of congruent triangles. **[25]**** ****[26]**

**What is a parallelogram example?**

In geometry, a quadrilateral is called a parallelogram. **[27]**** ****[28]** The opposite sides of a parallelogram are parallel and equal in length. Some examples of parallelograms are **rhombus, rectangle and square** .**[29]**** ****[30]**

**Does a parallelogram have four right angles?**

**A rectangle is** a parallelogram with four right angles, **[11]**** ****[31]** so all rectangles are also parallelograms and quadrilaterals. On the other hand, not all quadrilaterals and parallelograms are rectangles. A rectangle has all the properties of a parallelogram, plus the following: **[32]**** ****[33]** The diagonals are congruent.

**Is a rhombus a parallelogram?**

Every rhombus is simple (non-self-intersecting), and is a special case of

a parallelogram

and a kite. A rhombus with right angles is a square. ,

rhombus | |
---|---|

two rhombus | |

type | quadrilateral, parallelogram, kite |

edges and corners | 4 |

schlafli symbol | { } + { } {2_{α}} |

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