![]() ![]() ∠B + ∠C = 180° ( Interior angles on the same side of transversal is supplementary) Now, AB ∥ CD ( Opposite sides of a parallelogram are parallel), and BC is transversal. Hence, △ABC ≅ △DCB ( By SSS congruence rule) Thus in quadrilateral ABCD, both the opposite sides are equal.Īs we know, a square is a parallelogram with all sides equal and one right angle 90°.ĪB = DC ( Opposite sides of parallelogram are equal) Hence, △AOB ≅ △ COB ( By SAS congruence rule) Let ABCD be a quadrilateral, and ‘AC’, ‘BD’ are the two diagonals that bisect each other at ‘O’ Then we should prove whether all its sides are equal with one right angle. So, first, we need to prove the given quadrilateral is a parallelogram. Procedure: We know a square is a parallelogram with all sides equal and one angle 90°. Similarly, a rhombus is the only other special quadrilateral that has perpendicular bisecting diagonals. Let us take the example of a square, since its diagonals are both mutually bisecting and intersect at right angles, they are an example of quadrilaterals having perpendicular bisecting diagonals. the properties of mutually bisecting diagonals and that of the perpendicular bisecting diagonals, any quadrilateral fulfilling the criteria of both the above properties will satisfy the criteria to be a perpendicular bisecting diagonal. Since this property of a diagonal sums up the previous two properties, i.e. The perpendicular bisecting diagonals divide each other into half after they meet. Other than a rhombus, a square and a kite are examples of special quadrilaterals that have diagonals that are perpendicular to each other.ģ) Perpendicular Bisecting Diagonals: Also known as perpendicular bisectors, they are diagonals that form four right angles (90°) at the point of their intersection. This proves that the two diagonals in a rhombus meet each other at right angles. You will find all four angles formed through the intersection of the two diagonals equals 90°. After drawing both the diagonals, use the edge of a sheet of paper and place them in each one of the four angles. In other words, perpendicular diagonals form four right angles at the point of intersection. Other than a square, a rectangle, a parallelogram, and a rhombus are examples of special quadrilaterals that have diagonals that bisect each other.Ģ) Perpendicular Diagonals: They are diagonals that intersect each other at right angles (90°). This proves that both the diagonals have bisected each other into half. You will find both the sections of a diagonal to be equal. ![]() After drawing both the diagonals, measure each section of a diagonal. ![]() Types of Diagonals in Quadrilateralīased on their properties, diagonals of a quadrilateral can be of three broad types:ġ) Diagonals that Bisect Each Other: Also known as mutually bisecting diagonals, they divide each other into half after they meet. How Many Diagonals does a Quadrilateral HaveĪ quadrilateral is thus found to have two diagonals. The number of diagonals in a quadrilateral = 4 (4 – 3)/2 The number of diagonals in a polygon = n (n – 3)/2, where n = number of sides of the polygon Since, a quadrilateral is a four-sided polygon, we can obtain the number of diagonals in a quadrilateral by using the formula given below: ![]() Diagonal of Quadrilaterals How to Find the Diagonal of a Quadrilateral ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |