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 … Exercise 8.2 Page: 150. Show that the diagonals of a square are equal and bisect each other at right angles. Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square. Similarly, AOB ≅ DOC by SAS. 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. Hence, ∠ ACD = ∠ ACB ⇒ 2x + 4 = 5x - 8 {Given that ∠ ACD= 2x + 4 and ∠ ACB= 5x - 8 } ⇒ 3x = 12 ⇒ x = 4 (Answer) Ex 8.1 Class 9 Maths Question 2. Answer: Let the common ratio between the angles be x. CBSE Class 9 Maths Chapter 8 Quadrilaterals Exercise Questions with Solutions to help you to revise complete Syllabus and Score More marks. Now, the diagonal AC bisects angle C into ∠ ACD and ∠ ACB. Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus. Question 4. 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. Show that (i) It bisects \(\angle{C}\) also, (ii) ABCD is a rhombus. Given: ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Q5. ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see Fig. 1. Angle sum property of quadrilaterals and it’s proof Each side of a rhombus is 10 cm long and one of its diagonals measures 16 cm. In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (see figure). ABCD is a rhombus. NCERT Exemplar Class 9 Mathematics Chapter 8 Quadrilaterals, is provided here for students to prepare for exams and score good marks. i.e., the diagonals AC and PQ bisects each other. 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:. This will clear students doubts about any question and improve application skills while preparing for board exams. Get detailed answer of 6. Diagonal AC of a parallelogram ABCD bisects `\ /_A`. Solution: As we know that, the sum of the angles of a quadrilateral is 360° (Angle sum property of quadrilateral) As they are in ratio 3 : 5 : 9 : 13, so … Show that: (i) it bisects `angleC` also (ii) ABCD is a rhombus. (i) In … Question 1: The angles of quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral. Hence, AC is a diagonal. Show that is diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus. Show that (i) it bisects `\ /_C` also, (ii) ABCD is a rhombus. Diagonal AC of a parallelogram ABCD bisects A show that it bisects C also, ABCD is a rhombus - Math - Quadrilaterals Show that diagonal AC bisects ∠ A as well as ∠C and diagonal BD bisects ∠B as well as ∠D. So, the angles within the triangle ABC at A and C must both be 45º. Chapter-wise NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals solved by Expert Teachers as per NCERT (CBSE) Book guidelines. If a quadrilateral is a rhombus, then the diagonals of it will bisect each angle of the quadrilateral. Mathematics (www.tiwariacademy.com) (Chapter - 8) (Quadrilaterals) (Class - 9) Question 4: Show that the diagonals of a square are equal and bisect each other at right angles. The diagonals of a rhombus intersect at right angles. NCERT solutions for Class 9 Mathematics Textbook chapter 8 (Quadrilaterals) include all questions with solution and detail explanation. Question 1. 3. Here is one way of solving this. We're told that the diagonal AC bisects angles A and C. But all the interior angles of a rectrangle are 90º. To show, AC = BD, AO = OC and ∠AOB = 90° Proof, In ΔABC and ΔBAD, Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. In a quadrilateral ABCD, the diagonal AC bisects angle BAD and AB = BC = CD. Thus, in quadrilateral APCQ diagonals AC and PQ are such that OQ = OP and OA = OC. (v) Hence, APCQ is a parallelogram, which prove the part. Diagonal AC of a parallelogram ABCD bisects \(\angle{A}\) (see figure). 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 Diagonals of a Parallelogram Abcd Intersect at O. (ii) diagonal BD bisects ∠B as well as ∠D. To Prove: (i) ABCD is a square. Find the length of the other diagonal and hence find the area of the rhombus. If the diagonals of a parallelogram are equal, then show that it is a rectangle. Solution 12 Question 13 The angles of quadrilateral are in the ratio 3:5:9:13. 10. ̅̅̅̅ interse ABCD is a rhombus. Show that the line segments AF and EC trisect the diagonal BD. Solution. We will use triangle congruence to show that the angles are equal, and rely on the Side-Side-Side postulate because we know all the sides of a rhombus are equal. Show that (i) AAPB ACQD (ii) AP = CQ The diagonal AC divides the rectangle into two triangles ABC and ACD. 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. 4 In a parallelogram, the diagonals bisect each other. Since the figure is a parallelogram BC// to AD and
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