If a quadrilateral is a rhombus, then the diagonals of it will bisect each angle of the quadrilateral. The angles of quadrilateral are in the ratio 3:5:9:13. Hence, ABCD is a rhombus. Show that diagonal AC bisects angle A as well as the angle C and diagonal BD bisects angle B as well as angle D? Similarly, AOB ≅ DOC by SAS. 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. Hence, ∠ ACD = ∠ ACB ⇒ 2x + 4 = 5x - 8 {Given that ∠ ACD= 2x + 4 and ∠ ACB= 5x - 8 } ⇒ 3x = 12 ⇒ x = 4 (Answer) Diagonal AC of a parallelogram ABCD bisects \(\angle{A}\) (see figure). Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus. ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see Fig. 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 diagonal AC bisects ∠ A as well as ∠C and diagonal BD bisects ∠B as well as ∠D. Show that (i) It bisects \(\angle{C}\) also, (ii) ABCD is a rhombus. ABCD is a rhombus. Thus, in quadrilateral APCQ diagonals AC and PQ are such that OQ = OP and OA = OC. (iii) DO = DB [∵ diagonals of a rhombus bisects each other] ∴ AOD ≅ BOC by SAS. Show that (i) it bisects `\ /_C` also, (ii) ABCD is a rhombus. This discussion on 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. ̅̅̅̅ interse asked Sep 22, 2018 in Class IX Maths by muskan15 ( -3,443 points) quadrilaterals This will clear students doubts about any question and improve application skills while preparing for board exams. Given: ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. 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). Question 1. Solution. Find all the angles of the quadrilateral. AC is a diagonal. Show that: (i) it bisects `angleC` also (ii) ABCD is a rhombus. (i) In … 3. Given diagonal AC bisects
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