Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square. Question 4. CBSE Class 9 Maths Chapter 8 Quadrilaterals Exercise Questions with Solutions to help you to revise complete Syllabus and Score More marks. Mathematics ( (Chapter - 8) (Quadrilaterals) (Class - 9) Question 4: Show that the diagonals of a square are equal and bisect each other at right angles. (iii) DO = DB [∵ diagonals of a rhombus bisects each other] ∴ AOD ≅ BOC by SAS. NCERT Exemplar Class 9 Mathematics Chapter 8 Quadrilaterals, is provided here for students to prepare for exams and score good marks. asked Sep 22, 2018 in Class IX Maths by muskan15 ( -3,443 points) quadrilaterals Q5. This will clear students doubts about any question and improve application skills while preparing for board exams. AC is a diagonal. 1. Important Questions for CBSE Class 9 Mathematics Chapter 2 Quadrilaterals The topics and sub-topics in Class 9 Maths Chapter 8 Quadrilaterals: Quadrilaterals Introduction Angle Sum Property Of A Quadrilateral Types Of Quadrilaterals Properties Of A Parallelogram Another Condition For A Quadrilateral To Be A Parallelogram The MidPoint Theorem Summary IMPORTANT QUESTIONS VERY SHORT … Each side of a rhombus is 10 cm long and one of its diagonals measures 16 cm. Now, the diagonal AC bisects angle C into ∠ ACD and ∠ ACB. Thus, in quadrilateral APCQ diagonals AC and PQ are such that OQ = OP and OA = OC. The angles of quadrilateral are in the ratio 3:5:9:13. If a quadrilateral is a rhombus, then the diagonals of it will bisect each angle of the quadrilateral. In a quadrilateral ABCD, the diagonal AC bisects angle BAD and AB = BC = CD. (i) In … ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see Fig 8.29). The diagonal AC divides the rectangle into two triangles ABC and ACD. ∴ Diagonal AC = Diagonal BD. Similarly, AOB ≅ DOC by SAS. Let ABCD be a square and its diagonals AC and BD intersect each other at O. 3. Find the length of the other diagonal and hence find the area of the rhombus. Hence, We will do this first for the angles ∠BAC ≅ ∠DAC and ∠BCA ≅ ∠DCA, following the exact same proof we did for a kite , and then we will repeat the process for the other two pairs of angles, using the other diagonal. Show that (i) AAPB ACQD (ii) AP = CQ Show that (i) It bisects \(\angle{C}\) also, (ii) ABCD is a rhombus. Solution 12 Question 13 This discussion on ABCD is a rhombus. The diagonals of a rhombus intersect at right angles. Question 1. Now, In AOD and DOC (i) AD = DC [∵ all sides of a rhombus are equal] (ii) ∠AOD = ∠DOC = 90 o [∵ diagonals of a rhombus intersects each other at right angles] (iii) DO is the common side. Angle sum property of quadrilaterals and it’s proof Show that: (i) it bisects `angleC` also (ii) ABCD is a rhombus. Chapter-wise NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals solved by Expert Teachers as per NCERT (CBSE) Book guidelines. Ex 8.1 Class 9 Maths Question 2. We're told that the diagonal AC bisects angles A and C. But all the interior angles of a rectrangle are 90º. Show that is diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus. Prove that the other diagonal, BD, bisects angle ADC. 10. Show that the line segments AF and EC trisect the diagonal BD. Show that diagonal AC bisects ∠ A as well as ∠C and diagonal BD bisects ∠B as well as ∠D. 4 In a parallelogram, the diagonals bisect each other. Show that diagonal AC bisects angle A as well as the angle C and diagonal BD bisects angle B as well as angle D? 8.21). These exemplar problems have been designed according to the CBSE syllabus (2020-2021) for 9th standard by our experts, which covers the following topics of chapter Quadrilaterals given below:. (ii) diagonal BD bisects ∠B as well as ∠D. In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (see figure). Diagonal AC of a parallelogram ABCD bisects \(\angle{A}\) (see figure). Find all the angles of the quadrilateral. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D. Given: ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. If you have any query regarding Karnataka Board Class 9 Maths Chapter 7 Quadrilaterals Exercise 7.1, drop a comment below and we will get back to you at the earliest. So, the angles within the triangle ABC at A and C must both be 45º. The Diagonals of a Parallelogram Abcd Intersect at O. Diagonal AC of a paraleligram ABCD bisects `angleA` (sec figure). Given diagonal AC bisects