Why or why not? The diagonals of a quadrilateral ABCD are perpendicular to each other. Give reason for your answer. answered Dec 23, 2017 by ashu Premium (930 points) Given: A quadrilateral ABCD whose diagonals AC and BD are perpendicular to each other at O. P,Q,R and S are mid points of side AB, BC, CD and DA respectively are joined are formed quadrilateral PQRS. Any isosceles triangle, if that side's equal to that side, if you drop an altitude, these two triangles are going to be symmetric, and you will have bisected the opposite side. Given : MNPQ is a parallelogram whose diagonals are perpendicular. If the diagonals of a quadrilateral bisect each other at right angles , then name the quadrilateral . A quadrilateral whose all sides, diagonals and angles are equal is a (a) square (b) trapezium (c) rectangle (d) rhombus. 37 If the adjacent angles of a parallelogram are equal, then the parallelogram is a (a) rectangle (b) trapezium (c) rhombus (d) None of these Solution. Diagonals of a quadrilateral PQRS bisect each other. Proof : In ABC, P and Q are mid - points of AB and BC respectively. ∴ Their diagonals … Properties of Trapezium; One pair of opposite sides is parallel. Hence the point of intersection will be the centre of the circle. d. If the adjacent sides of a parallelogram are equal , then the parallelogram is called a -----e.The quadrilateral having one pair of opposite sides parallel is called a -----. The diagonals of a quadrilateral ABCD are perpendicular to each other. This means that they are perpendicular. Every square is a parallelogram in which diagonals are congruent and bisect the angles. Textbook Solutions 5346. ∴ Their diagonals are perpendicular bisectors of each other. A quadrilateral with exactly one pair of parallel sides is a trapezoid If the diagonals of a parallelogram are perpendicular and not congruent, then the parallelogram is c. In convex polygon each interior angle is -----. Each interior angle measures 90°. The diagonals of a quadrilateral ABCD intersects each other at the point O such that AO/BO = CO/DO ,So that ABCD is a trapezium. Explain why this statement is true or sketch a counterexample. In Euclidean geometry, an orthodiagonal quadrilateral is a quadrilateral in which the diagonals cross at right angles.In other words, it is a four-sided figure in which the line segments between non-adjacent vertices are orthogonal (perpendicular) to each other. ∠AOB = 30°, AC = 24 and BD = 22. d. rhombus. The quadrilateral with vertices (0,3), (2,0), (0,-1), (-2,0) has congruent, perpendicular diagonals--but it isn't a square. Diagonals intersect each other in the same ratio. Thus, PQRS is a parallelogram whose one angle is 90°. ABCD is a quadrilateral with diagonals AC and BD. The diagonals are then said to be 'perpendicular bisectors'. But, if both the diagonals are perpendicular bisectors of each other. We can prove it by proving (1): first ABCD a … And you see the diagonals intersect at a 90-degree angle. ∴ Opposite sides of quadrilateral PMON parallel . ABCD is a rhombus and AB is produved to E and F such that AE=AB=BF prove that ED and FC are perpendicular to each other. The diagonals of a quadrilateral ABCD are perpendicular to each other. A quadrilateral whose all sides, diagonals and all angles are equal is called a -----. A parallelogram, the diagonals bisect each other. The length of each side of the rhombus is. Proof that the diagonals of a rhombus are perpendicular Continuation of above proof: Corresponding parts of congruent triangles are congruent, so all 4 angles (the ones in the middle) are congruent. Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Diagonals of quadrilateral ABCD bisect each other. This is because its diagonals form a right angle at its center. The diagonals are perpendicular to and bisect each other. If the diagonals of a quadrilateral bisect each other at right angles, then the figure is a . Thus , one pair of opposite sides of quadrilateral PQRS are parallel and equal . b. 10 cm; 12 cm; 9cm; 8cm; Solution 7 . For a rhombus, where all the sides are equal, we've shown that not only do they bisect each other but they're perpendicular bisectors of each other. Adjacent: It is the side adjacent to the angle being considered. Show that the quadrilateral formed by joining the mid-points of its sides is a rectangle. Line ef,fg,gh, eh and are congruent Quadrilateral ABCD has coordinates A (3, 5), B (5, 2), C (8, 4), D (6, 7). Is this statement true? The area of quadrilateral ABCD is: The diagonals AC and BD of a cyclic quadrilateral ABCD intersect at P. Let O be the circumcentre of ∆APB and H be the orthocentre. Diagonals of a quadrilateral ABCD bisect each other. B) It is a parallelogram with perpendicular diagonals. Do a kite's diagonals bisect angles? Well, we can look at the triangles formed by drawing the diagonals. A quadrilateral whose diagonals bisect each other and are perpendicular can be a rhombus or a square. Is such a quadrilateral always a rhombus? Diagonals of a quadrilateral are perpendicular to each other. if you think of 3dimensions, there could be 3 lines all perpendicular to each other (x,y,z axes for example) then that would be an example of mutually perpendicular, but I think you will be able to imagine that for 3 vectors a,b and c, a can be perpendicular to b and b to c, but it is not then general that c is perpendicular to a . If there is no information about the angles of the quadrilateral, we cannot say for certainty that it is a square. Diagonals AC and BD of a parallelogram ABCD intersect each other at O. c. rectangle. A rhombus is a quadrilateral where all 4 sides have the same length. In the above image, ABCD is a cyclic quadrilateral & its diagonals AC & BD are perpendicular to each other. 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