In a parallelogram opposite angles are equal

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Measurement and Geometry : Module 20 Years : PDF Version of module. In contrast, there are many categories of special quadrilaterals. Apart from cyclic quadrilaterals, these special quadrilaterals and their properties have been introduced informally over several years, but without congruence, a rigorous discussion of them was not possible. Each congruence proof uses the diagonals to divide the quadrilateral into triangles, after which we can apply the methods of congruent triangles developed in the module, Congruence.

In a parallelogram opposite angles are equal

The opposite angles of a parallelogram are equal and the consecutive angles of a parallelogram are supplementary. Let us read more about the properties of the angles of a parallelogram in detail. A parallelogram is a quadrilateral with equal and parallel opposite sides. There are some special properties of a parallelogram that make it different from the other quadrilaterals. Observe the following parallelogram to relate to its properties given below:. The theorems related to the angles of a parallelogram are helpful to solve the problems related to a parallelogram. Two of the important theorems are given below:. Hence proved, that opposite angles in any parallelogram are equal. The converse of the above theorem says if the opposite angles of a quadrilateral are equal, then it is a parallelogram. Let us prove the same. This shows that the consecutive angles are supplementary. Hence, it means that AD BC.

Hence, it will become a rectangle. Rectangles Definition of a rectangle A rectangle is a quadrilateral in which all angles are right angles. We know that in any parallelogram, the opposite angles are equal.

A quadrilateral whose two pairs of sides are parallel to each and the four angles at the vertices are not equal to the right angle, and then the quadrilateral is called a parallelogram. Also, the opposite sides are equal in length. Learn more about the parallelogram here. Also, we have different theorems based on the angles of a parallelogram. They are explained below along with proofs.

The properties of a parallelogram help us to identify a parallelogram from a given set of figures easily and quickly. Before we learn about the properties, let us first know about parallelograms. It is a four-sided closed figure with equal and parallel opposite sides and equal opposite angles. Let us learn more about the properties of parallelograms in detail in this article. A parallelogram is a type of quadrilateral in which the opposite sides are parallel and equal.

In a parallelogram opposite angles are equal

A parallelogram is a two-dimensional geometrical shape whose sides are parallel to each other. It is a type of polygon having four sides also called quadrilateral , where the pair of parallel sides are equal in length. The Sum of adjacent angles of a parallelogram is equal to degrees. In geometry, you must have learned about many 2D shapes and sizes such as circles, squares, rectangles, rhombus, etc. All of these shapes have a different set of properties. Also, the area and perimeter formulas of these shapes vary from each other and are used to solve many problems. Let us learn here the definition, formulas and properties of a parallelogram. A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. Also, the interior angles on the same side of the transversal are supplementary.

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Let us prove this property considering the following given fact and using the same figure. A parallelogram is a quadrilateral with equal and parallel opposite sides. Draw two intersecting lines, then draw two circles with different radii centred on their intersection. Post My Comment. Fair enough. Let ABCD be a rectangle. And to do that, we just have to realize that we have some parallel lines, and we have some transversals. PT and QR are the diagonals of the parallelogram. The parallelogram ABQP shows, for example, that. For example, when two forces are combined, a parallelogram can be drawn to help compute the size and direction of the combined force. Complete this to a construction of the parallelogram ABCD , justifying your answer. Already booked a tutor? J oin the diagonal AC.

A parallelogram is a quadrilateral in which the opposite sides are parallel and equal. Parallelograms are classified into three main types: square, rectangle, and rhombus, and each of them has its own unique properties. In this article, let us learn about the parallelogram shape , the parallelogram definition , the different types of parallelograms , how to find the area of a parallelogram and parallelogram examples.

Sam De Laurentis. Privacy Policy. Theorems on Parallelogram Properties 4. There are two important properties of the diagonals of a parallelogram. Learn Practice Download. Want to join the conversation? Hence, it is proved that the opposite angles of a parallelogram are equal. Theorems Related to Angles of a Parallelogram 3. Posted 4 years ago. The properties of diagonals of a parallelogram are as follows:. View Result. Now, let us expand our knowledge by learning about the properties of diagonals of parallelograms in the following section.. Your Mobile number and Email id will not be published.