![]() By knowing the length and breadth of the parallelogram, we can get the perimeter of a parallelogram. The perimeter of a parallelogram is calculated as the total distance of the boundaries of the parallelogram. The area of the Parallelogram can be calculated as Area = Base × Height Perimeter of Parallelogram The area of the Parallelogram totally depends on the Base and height of the Parallelogram. Each diagonal bisects the parallelogram into two congruent triangles.Parallelogram law: The sum of squares of all the sides of a parallelogram is always equal to the sum of squares of its diagonals.If one angle of a parallelogram is a right angle, then all other angles are right angles.Furthermore, The two diagonals bisect each other.The consecutive angles are supplementary.Also, the opposite sides are parallel and congruent.The opposite angles of a parallelogram are congruent.Properties of ParallelogramĬheck the below properties of a parallelogram and solve the related problems easily by applying the same. Furthermore, the sum of the interior angles is 360 degrees. When you add the same side of the transversal angles, you can get 180 degrees. Its opposite interior angles always equal and the angles on the same side of the transversal are always supplementary with each other. Also, the interior angles of the parallelogram should always equal. All the parallel sides of the Parallelogram are equal in length. It consists of four sides and two pairs of parallel sides. Shape of ParallelogramĪ parallelogram shape is a two-dimensional shape. Similarly, ∠B & ∠C are supplementary angles. Because ∠A & ∠D are interior angles present on the same side of the transversal. Also, CD = AB and BC = AD.Īlso, ∠A & ∠D are supplementary angles. Or else, if a parallelogram has one parallel side and the other two sides are non-parallel, then it treats as a trapezium.įrom the above figure, ABCD is a parallelogram, where CD || AB and BC || AD. If in case, the sides of the parallelogram become equal, then it treats as a rhombus. The sum of all the interior angles becomes 360 degrees in a parallelogram.Ī rectangle and square also consist of similar properties of a parallelogram. The interior angles of the parallelogram on the same side of the transversal are supplementary. Properties of a Rectangle Rhombus and SquareĪ parallelogram called a quadrilateral that has two pairs of parallel sides.Practice as much as you can and solve all the problems easily. All you need to do is simply tap on the quick links and avail the underlying concept within. Have a glance at the list of Parallelogram Concepts available below and use them for your reference. Also, the perimeter of the parallelogram depends on the length of its four sides. The area of the parallelogram always depends on its base and height. While adding the adjacent angles of a parallelogram, you will get 180 degrees. ![]() Furthermore, the interior opposite angles also equal in measurement. The pair of parallel sides are always equal in length of a parallelogram. The parallelogram has four sides and also it is called a quadrilateral. ![]() Therefore, the correct answer is (4) All of them are true.Parallelogram consists of a flat shape that has two opposite & parallel sides with equal length. Using the properties of similar triangles:Ĭ D A D = CF A E ⇒ A E A D = CF C D (2)Ĭombining the established relationships (1) and (2), we deduce: Hence, triangles A D E and C D F are also similar by the AA (Angle-Angle) similarity criterion. We know that angle ∠ A D E is congruent to angle ∠ C D F (corresponding angles of parallel lines A B and C D), and angle ∠ D A E is congruent to angle ∠ D CF (alternate interior angles of the parallel lines A D and BC). Now, let's observe another pair of triangles - A D E and C D F. Since A D = BC (opposite sides of a parallelogram), we can write: That is:īC A D = BE A E ⇒ A E A D = BE BC (1) Since triangles A D E and BCE are similar, the ratios of their corresponding sides are equal. Step 4: Use the properties of similar triangles So, triangles A D E and BCE are similar by the AA (Angle-Angle) similarity criterion (two pairs of corresponding angles are congruent). Angles ∠ D A E and ∠ ECB are corresponding angles of parallel lines A B and C D ( A D ∥ CB) hence they are congruent. Let's observe another pair of angles in these triangles: Step 3: Prove triangles ADE and BCE are similarįrom step 2, we have angle ∠ A D E is congruent to angle ∠ BCE. Since A D ∥ BC, we know that angle ∠ A D E is congruent to angle ∠ BCE (alternate interior angles are congruent). A B ∥ C D (opposite sides are parallel) Step 2: Use the properties of the parallelogram We know that when a quadrilateral is a parallelogram, the opposite sides are equal and parallel ( A B ∥ C D, A D ∥ BC).
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