To prove this statement we need to use the result that the diagonals of a parallelogram (which the rhombus is a particular kind of) bisect each other. Given: Quadrilateral ABCD is a CPCTC 8. Transcript. All Right ’s S 7. prove:AC bisects angle BAD and angel BCD. In the given figure, O is the center of the circle. In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see figure). AD CD 3. NCERT Solutions for Class 9 Maths includes solutions to all the questions given in the NCERT Maths textbook. To Prove: Quadrilateral ABCD is a square. 6. converse of Alternate Interior Angles Theorem 7. m∠BEC = m∠AED Vertical Angles Theorem 8. Abcd is a Parallelogram in Which Diagonal Ac Bisects ∠Bad. Defn A 6. To Prove: (i) ABCD is a square. prove that BC=CD - 1753581 3 and 4 right angles 5. [∵ AC = BD (given)] And, in ∆BCD, by mid-point theorem RQ || BD and RQ = BD = AC …(v) From equations (iv) and (v), we get SP || RQ and SP = RQ = AC …(vi) Now, from equations (iii) and (vi), we get PQ = SR = SP = RQ Thus, all four sides (RBSESolutions.com) are equal. (ii) ABCD is a rhombus.Proof: (i) In ∆ADC and ∆CBA,AD = CB| Opp. Delhi - 110058. P is any point on the side AB. In a quadrilateral abcd bisecter of angle c and d intersect at o. In the given figure, AC is a diameter of the circle with centre O. Chord BD is perpendicular to AC. D is the midpoint of 2. 414-3 Rhombus and Square On 1 — 2, refer to rhombus ABCD where diagonals AC and BD intersect at E. Given rho bus ABCD where diagonals AC and BD intersects at E. Proof: In quadrilateral ABCD, AC bisects BD (given) So, diagonals bisect each other ∴ ABCD is a Parallelogram (In a parallelogram, diagonals bisect each other) Now, Opposite angles of Parallelogram are equal Now, ∠BAD = ∠BCD and ∠ABC = ∠ADC Also, ABCD is a cyclic quadrilateral, ∴ Sum of opposite angles is 180° ∠BAD + ∠BCD = 180° ∠BCD + ∠BCD = 180° 2 ∠BCD = 180° ∠ BCD = … given 2. In a two column proof, prove that ABCD is a rhombus. All solutions are explained using step-by-step approach. Question 1. Int. so same rule is applied here.i.e