Diagonals of rectangle bisect each other. Moreover, the opposite angles in a parallelogram are equal and its diagonals bisect each other. Answers: 2 on a question: Fill in the blanks :- a. I am a quadrilateral with exactly one pair of opposite sides are parallel. f. _____ is a quadrilateral whose all sides and opposite angles are equal and diagonals bisect each other at right angles. Length of diagonals of a rhombus is not the same. two equal diagonals \[AC=BD\] diagonals that are perpendicular to each other \[AC \perp BD\] diagonals that bisect each other. Answered Rectangle. (a) Triangle (b) Square (c) Rhombus (d) None of these (b) Square. q A quadrilateral whose all sides are equal, opposite angles are equal and the diagonals bisect each other at right angles is a _____. No rhombi are rectangles. [7] Silvester (2006) gives further connections between equidiagonal and orthodiagonal quadrilaterals, via a generalization of van Aubel's theorem. Theorem 1: If the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallelogram. Diagonals intersect at right angles. Completing the CAPTCHA proves you are a human and gives you temporary access to the web property. Any quadrilateral that is not self-intersecting is a simple quadrilateral. If you are at an office or shared network, you can ask the network administrator to run a scan across the network looking for misconfigured or infected devices. In a cyclic quadrilateral, the ratio of the diagonals equals the ratio of the sum of products of sides that share the diagonal’s end points. Length of diagonals of a rhombus is not the same. Which one of the following is a regular quadrilateral? If ABCD is a cyclic quadrilateral, then AB x CD + AB x BC = AC x BD. A quadrilateral whose all sides, diagonals and all angles are equal is called a -----------. Square is a rectangle whose all sides are equal. ∴ Their diagonals are perpendicular bisectors of each other. c) Kite. by Jennifer Kahle. b. A parallelogram is equidiagonal if and only if it is a rectangle,[6] and a trapezoid is equidiagonal if and only if it is an isosceles trapezoid. The diagonals of a quadrilateral can determine whether it is a parallelogram, a rectangle, a rhombus, etc.. We will list and prove the main theorems here. Equidiagonal quadrilaterals were important in ancient Indian mathematics, where quadrilaterals were classified first according to whether they were equidiagonal and then into more specialized types.[1]. 1. The sum of four interior angles is equal to 360°. False. Log in. Square. ABCD is a quadrilateral whose diagonal AC divides it into two parts equal in area, then ABCD is: from Mathematics Areas of Parallelograms and Triangles Class 9 … A square is also a parallelogram as the opposite sides are parallel to each other. In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. But the angles of a quadrilateral add to 360 o, and therefore each of these 4 angles must be 90 o. Theorem 3: If the diagonals of a quadrilateral bisect each other and are perpendicular then the quadrilateral is a rhombus. 6 Fill in the blanks : a) A quadrilateral whose all the sides, diagonals and angles are equal is _____ b) Diagonals of a rectangle _____ c) Diagonals of a rhombus _____ d) Both the diagonals of a rhombus are _____ in length e) The - Math - Understanding Elementary Shapes Fig. • The opposite sides are parallel. Diagonal Line. a quadrilateral and the results of parallel lines intersected by a transversal, we can see that the converse is also true. It has rotational symmetry of order two. A square is a special type of parallelogram whose all angles and sides are equal. Both diagonals of a rhombus intersect at 90º to each other. 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