The sum of adjacent angles of a parallelogram is -----. So we know that PQRS is a parallelogram with ∠ QPS = 90. If ∠P = 40°, determine ∠Q. 36 Length of one of the diagonals of a rectangle whose sides are 10 cm and 24 cm is (a) 25 cm (b) 20 cm (c) 26 cm (d) 3.5 cm Solution. A rhombus is a parallelogram whose diagonals are perpendicular to each other. Explanation: A parallelogram whose diagonals are perpendicular is a rhombus or a square. d. rhombus. The quadrilateral that must have diagonals that are congruent and perpendicular is the square. b. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students. 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. 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. The longer diagonal of a kite bisects the shorter one. Each interior angle measures 90°. Diagonals of a quadrilateral are perpendicular to each other. Give a figure to justify 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. The diagonals of a quadrilateral ABCD are perpendicular to each other. Other names for quadrilateral include quadrangle (in analogy to triangle), tetragon (in analogy to pentagon, 5-sided polygon, and hexagon, 6-sided polygon), and 4-gon (in analogy to k-gons for arbitrary values of k).A quadrilateral with vertices , , and is sometimes denoted as . 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. When we have a four-sided figure whose diagonals are perpendicular, this means that the diagonals intersect to create a 90-degree angle. Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. We can prove it by proving (1): first ABCD a … Diagonals intersect each other in the same ratio. ∠AOB = 30°, AC = 24 and BD = 22. 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 -----. Prove that the quadrilateral formed by joining the midpoints of its sides is a rectangle. Rectangle and square have their all angles equal. Question. Question 7. Well, we can look at the triangles formed by drawing the diagonals. Problem 25 Easy Difficulty "If the two diagonals of a quadrilateral are perpendicular, then the quadrilateral is a rhombus." ∴ PQ || AC and PQ = 1 / 2 AC ---- (i)  [mid point theorem]. The diagonals of a quadrilateral ABCD are perpendicular to each other. 10 cm; 12 cm; 9cm; 8cm; Solution 7 . Explain why this statement is true or sketch a counterexample. If the diagonals of a quadrilateral bisect each other at right angles , then name the quadrilateral . 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. The diagonals are perpendicular to and bisect each other. Diagonals of a quadrilateral ABCD bisect each other. Name the Quadrilaterals Whose Diagonals Are Perpendicular Bisectors of Each Other . The intersection of the diagonals of a kite form 90 degree (right) angles. If ∠A= 35°, determine ∠B. Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Diagonals of quadrilateral ABCD bisect each other. This leads to the fact that they are all equal to 90 degrees, and the diagonals are perpendicular to each other. ∴ Their diagonals … Is ABCD a parallelogram? Given : MNPQ is a parallelogram whose diagonals are perpendicular. Diagonals AC and BD of a parallelogram ABCD intersect each other at O. Diagonals of a quadrilateral PQRS bisect each other. 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. c. In convex polygon each interior angle is -----. If ∠A= 35°, determine ∠B. ∴ Their diagonals are perpendicular bisectors of each other. A quadrilateral whose diagonals bisect each other at right angles is a rhombus. Hence the point of intersection will be the centre of the circle. asked Aug 2, 2020 in Quadrilaterals by Rani01 (52.4k points) quadrilaterals; practical geometry; class-8; 0 votes. Diagonals of a quadrilateral are perpendicular to each other. If there is no information about the angles of the quadrilateral, we cannot say for certainty that it is a square. Why or why not? We know that the angles formed by the diagonals are right angles (because they are perpendicular). Prove that the quadrilateral formed by joining the midpoints of its sides is a rectangle. Ex 5.5, 1 Which of the following are models for perpendicular lines : (b) The lines of a railway track Here, the t Can we construct a quadrilateral where the diagonals are perpendicular bisectors where the side lengths are different? Is this statement true? And you see the diagonals intersect at a 90-degree angle. The diagonals bisect each other: AO = OC and BO = OD. So we've just proved-- so this is interesting. To prove : MNPQ is a rhombus. The quadrilateral with vertices (0,3), (2,0), (0,-1), (-2,0) has congruent, perpendicular diagonals--but it isn't a square. Properties of Trapezium; One pair of opposite sides is parallel. Give reason for your answer. ∴ SR || AC and SR = 1 / 2 AC --- (ii) [mid point theorem], From (i) and (ii) , we have  PQ || SR and PQ = SR. c. rectangle. In △ABD, P and S are mid points of AB and AD respectively . CBSE CBSE Class 8. A quadrilateral whose all sides, diagonals and angles are equal is a (a) square (b) trapezium (c) rectangle (d) rhombus. Thus , one pair of opposite sides of quadrilateral PQRS are parallel and equal . ABCD is a quadrilateral with diagonals AC and BD. Quadrilateral EFGH is a square7. Then in such case , we can prove that ABCD is a square. In the given figure ABCD is a quadrilateal whose diagonals intersect at O. Give a figure to justify your answer. Adjacent: It is the side adjacent to the angle being considered. B) It is a parallelogram with perpendicular diagonals. 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 -----. If a and b are the lengths of the diagonals of a rhombus, Area = (a* b) / 2; Perimeter = 4L; Trapezium The diagonals are perpendicular bisectors of each other. But, if both the diagonals are perpendicular bisectors of each other. Proof : In ABC, P and Q are mid - points of AB and BC respectively. Solution 6. But its point of intersection is not the centre of the circle. To Prove : PQRS is a rectangle. The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Question Bank Solutions 4773. b. parallelogram . Every square is a rectangle and a rhombus. We also know that all of the triangles will have 1 side equal to … Thus, PQRS is a parallelogram whose one angle is 90°. Textbook Solutions 5346. If the diagonals of a quadrilateral bisect each other at right angles, then the figure is a . Therefore, it is proved that the quadrilateral formed by joining the midpoints of its sides is a rectangle. If ∠A = 35degree, determine ∠B. 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 . Question. a. trapezium. Do a kite's diagonals bisect angles? This is because its diagonals form a right angle at its center. A rhombus is a quadrilateral where all 4 sides have the same length. Show that the quadrilateral formed by joining the mid-points of its sides is a rectangle. So by the same argument, that side's equal to that side, so the two diagonals of any rhombus are perpendicular to each other and they bisect each other… A quadrilateral is a polygon in Euclidean plane geometry with four edges (sides) and four vertices (corners). Question 8. Diagonals are equal and are perpendicular bisectors of each other. In the above image, ABCD is a cyclic quadrilateral & its diagonals AC & BD are perpendicular to each other. A parallelogram, the diagonals bisect each other. The diagonals of a quadrilateral ABCD are perpendicular to each other. 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. 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 Diagonals of a parallelogram are perpendicular to each other. (iii) are equal The diagonals of a quadrilateral are equal if its all the angles are equal . 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. Proof : In △ABC, P and Q are mid - points of AB and BC respectively. All sides are congruent, opposite sides are parallel, and adjacent sides are perpendicular. Diagonals of a quadrilateral ABCD bisect each other. 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 O such that OA : OC = 3: 2. (a) We know that, the adjacent angles of a parallelogram are supplementary, i.e. Ex 3.4, 4 Name the quadrilaterals whose diagonals. The length of each side of the rhombus is. 1 answer. Show that ABCD is a parallelogram. A quadrilateral whose diagonals bisect each other and are perpendicular can be a rhombus or a square. Adjacent angles are supplementary (For eg., ∠A + ∠B = 180°). Further, in  △ACD, R and S are mid points of CD and DA respectively. The diagonals are then said to be 'perpendicular bisectors'. If the diagonals of a rectangle are perpendicular, then the rectangle is a square. 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 such a quadrilateral always a rhombus? We know that P and Q are the midpoints of AB and BC, We know that R and S are the midpoints of CD and AD, We know that a pair of opposite sides are equal in a parallelogram, We know that AC and BD are the diagonals intersecting at point O, We know that P and S are the midpoints of AD and AB, We know that opposite angles are equal in a parallelogram, So we know that PQRS is a parallelogram with ∠ QPS = 90o. 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