In a parallelogram opposite angles are equal

Measurement and Geometry : Module 20 Years :

If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Search for courses, skills, and videos. Theorems concerning quadrilateral properties. About About this video Transcript. Sal proves that opposite angles of a parallelogram are congruent. Created by Sal Khan.

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. Similarly, we can show that AB CD. Therefore ABCD is a parallelogram.

No, according to the theorems based on the angles of a parallelogram, the opposite angles are not supplementary, they are equal. Direct link to Antheni M. This means that a rectangle is a parallelogram, so:.

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.

A Quadrilateral has four-sides , it is 2-dimensional a flat shape , closed the lines join up , and has straight sides. Also see this on Interactive Quadrilaterals. Try drawing a quadrilateral, and measure the angles. Some types are also included in the definition of other types! For example a square , rhombus and rectangle are also parallelograms. See below for more details. Also opposite sides are parallel and of equal length. A rhombus is a four-sided shape where all sides have equal length marked "s". Another interesting thing is that the diagonals dashed lines meet in the middle at a right angle.

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.

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We can construct a rectangle with given side lengths by constructing a parallelogram with a right angle on one corner. Yes, the opposite angles of a parallelogram are congruent. In geometry two shapes are congruent if they have the same shape or size. The opposite angles of a parallelogram are equal and the consecutive angles of a parallelogram are supplementary. Further, these theorems are also supportive of understanding the concepts in other quadrilaterals. And to do that, we just have to realize that we have some parallel lines, and we have some transversals. Your Mobile number and Email id will not be published. No, according to the theorems based on the angles of a parallelogram, the opposite angles are not supplementary, they are equal. We have:. And actually, we could extend this point over here. If one pair of opposite sides of a quadrilateral are equal and parallel, then the quadrilateral is a parallelogram. Technically, point D is not an angle : Since Sal is talking about parallelograms, the angle BDC the angle defined by the line segments BD and CD isn't necessarily a right angle, but it's not impossible for it to be a right angle.

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.

That means that the two figures are congruent. Thus, by ASA criterion , the two triangles are congruent. Join AM. PDF Version of module. AD BC. You can't assume that BDC is a right angle, because if you did, you'd only prove that the opposite angles of a parallelogram are equal if one of the angles is a right angle from which would follow that the other three angles are right angles too. Just wondering. About About this video Transcript. Maths Questions. The opposite sides of a rectangle are equal and parallel. Your result is as below. United Kingdom. The quadrilateral formed by joining the four points where the circle cuts the lines is a rectangle because it has equal diagonals that bisect each other. Want to join the conversation? Learn Angles Of A Parallelogram with tutors mapped to your child's learning needs.