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Diagonal of Parallelogram Formula
A quadrilateral with equal pairs of opposite sides and angles is referred to as a parallelogram. It has a pair of opposite sides that are parallel to one another. The Diagonal Of Parallelogram Formula inner angles are supplementary, meaning that their sum equals 180 degrees. A parallelogram’s diagonals are bisected by one another or divided into two equal portions. A parallelogram’s internal angles, to which the Diagonal Of Parallelogram Formula pertains, add up to 360 degrees.
A parallelogram is a twodimensional geometric shape with sides that are parallel to one another. It is a polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram to which the Diagonal Of Parallelogram Formula pertains, has adjacent angles that add up to 180 degrees.
Students must have studied a variety of 2D shapes, Diagonal Of Parallelogram Formula, and several figures in Geometry, including circles, squares, rectangles, rhombuses, etc. Each of these forms has a unique set of characteristics. Additionally, the Diagonal Of Parallelogram Formula is the difference between these shapes’ area and perimeter formulas, which are applied to various issues.
What is the Diagonal of Parallelogram?
A Diagonal Of Parallelogram Formula can be drawn by connecting the two nonadjacent vertices. It should be observed that a parallelogram’s two diagonals intersect one another, dividing it into congruent triangles.
There are four angles on the flat, twodimensional parallelogram. The internal angles on either side are equal. The transversal angles on the same side are supplementary, which means they sum to 180 degrees. As a result, a parallelogram’s internal angles add up to 360 degrees.
The qualities of a parallelogram are shared by the shapes of a square and a rectangle. Both have opposite sides that are parallel and equal to one another. Both shapes’ diagonals cut each other in half. A parallelogram is a unique type of geometrical figure where the adjacent sides are not the same length, but the opposite sides are parallel. Additionally, the Diagonal Of Parallelogram Formula and the angles are all 90 degrees. It is a trapezium if just one pair of its sides are parallel and the other two are not.
Diagonal of Parallelogram Formula
The length of a given parallelogram’s diagonals can be determined using the formula for a Diagonal Of Parallelogram Formula. Various parallelogram types have different formulas. A quadrilateral with opposite sides that are parallel and equal is known as a parallelogram. Due to the opposite side’s alignment and equality, they have equal angles on them. The Diagonal Of Parallelogram Formula that links a parallelogram’s opposite corners pertains to its diagonals.
Mathematical notions like polygons have been around for a very long time. Greek architects and mathematicians created mathematical models (statutes) preserved in museums to prove they were aware of regular polygons.
A polygon is a fundamental building block used in modelling and rendering in computer graphics. They are more specifically described in a database system that contains arrays of vertices (the coordinates of the geometric vertices and other polygonal attributes).
Properties of Diagonal of Parallelogram
When the opposing sides of a quadrilateral are parallel and equal, the shape is called a parallelogram. A Diagonal Of Parallelogram Formula has four angles at its vertices. The Diagonal Of Parallelogram Formula is easier to relate the angles and sides of a parallelogram when one is aware of its characteristics. Additionally, the qualities help calculate a parallelogram’s sides and angles.
The theorems on a Diagonal Of Parallelogram Formula properties define the guidelines for solving problems involving parallelograms. Diagonal Of Parallelogram Formula is simple to comprehend and use the properties of a parallelogram’s sides and angles to address various issues. Additionally, the Diagonal Of Parallelogram Formula help in comprehending the ideas in other quadrilaterals. The following list includes four important theorems concerning a parallelogram’s characteristics:
 A parallelogram’s opposite sides are equal.
 In a parallelogram to which the Diagonal Of Parallelogram Formula pertains, the opposing angles are equal.
 A parallelogram’s diagonals cut each other in half.
 A quadrilateral is a parallelogram if one set of opposite sides is equal and parallel.
Examples using Diagonal of Parallelogram Formula
Example 1: Find the length of the diagonals of the rhombus of side length 4 inches, if the interior angles are 120° and 60°.
Solution:
Given, Interior angle A = 120°, and angle B = 60°.
x = 4, y = 4
Using the diagonal of the parallelogram formula,
p=√x2+y2−2xycosAp=x2+y2−2xycosA
q=√x2+y2+2xycosAq=x2+y2+2xycosA
Putting the values in the formula for p:
p=√42+42−(2×4×4×cos60)=√32−16p=4p=42+42−(2×4×4×cos60)=32−16p=4
Now, doing the same for q,
q=√42+42+(2×4×4×cos60)=√32+16p=√48p=6.92q=42+42+(2×4×4×cos60)=32+16p=48p=6.92
Answer: The length of the diagonals are 4 in and 6.92 in.
Example 2: Calculate the length of the diagonal of a parallelogram with sides 4 units, 6 units, and an interior angle A equal to 60 degrees.
Solution:
Given, a = 4 units, b = 6 units, angle A = 60°
Using the diagonal of the parallelogram formula,
p=√x2+y2−2xycosAp=x2+y2−2xycosA
Putting the values in the formula for p:
p=√42+62−24p=42+62−24= √2828 = 5.291
Answer: Diagonal of parallelogram = 5.291 units.
Practice Questions on Diagonal of Parallelogram
Question 1:
Find the diagonal of a parallelogram with sides 3 cm, 5 cm, and angles of 45 degrees.
Solution:
Given a = 3 cm
b = 5 cm
angle A = 45°
Formula of diagonal is,
q = a2+b2−2abcosA
q = 32+52–2×3×5cos45
q = 34–30×0.707
q = √12.79
=3.576 cm
Diagonal of parallelogram = 3.576 cm.
FAQs (Frequently Asked Questions)
1. How to Determine the Diagonals of a Parallelogram without Angles?
Even without knowing the internal angles, it is still possible to compute the length of a Diagonal Of Parallelogram Formula. For instance, if the parallelogram is a rectangle, students are aware that the diagonals of a rectangle form a rightangled triangle. In this instance, the diagonal becomes the hypotenuse, allowing the Pythagoras theorem to determine the length of the diagonal if the length of the rectangle’s sides is known. The same procedure can be used if the provided parallelogram is a square.
2. Are a Parallelogram's Diagonals Equal?
A square, rectangle, and rhombus make up a parallelogram. A rhombus’ diagonals may not always be equal, although a square and a rectangle are.
3. Do a parallelogram's diagonals bisect one another?
Yes, a parallelogram’s diagonals are perpendicular to one another. This implies that a parallelogram’s diagonals divide into two equal parts.
4. What makes up the formula for the diagonal of a parallelogram?
When using the side lengths and any known angles in the parallelogram formula, it is possible to determine the length of the diagonals. The parallelogram’s sides and associated angles are thus included in its parts.
5. What is a parallelogram's diagonal?
The line segment connecting the parallelogram’s two nonadjacent vertices is known as the diagonal. It should be noted that a parallelogram can have two diagonals.
6. What are the parallelogram's characteristics in relation to the diagonals?
A Diagonal Of Parallelogram Formula has two significant characteristics. A parallelogram is split into two congruent triangles by its diagonal. Additionally, a parallelogram’s diagonals cut each other in half.
7. Can a parallelogram be used to describe a rectangle?
A rectangle has equal and parallel opposite sides. Therefore, a rectangle can be referred to as a parallelogram since it meets all the criteria for one.