∠sBut ∠CAB = ∠CAD∴ ∠ACD = ∠CAD∴ AD = CD| Sides opposite to equal angles of a triangle are equal∴ ABCD is a square. Show that (i) It bisects $$\angle{C}$$ also, (ii) ABCD is a rhombus. Prove: AB ≅ BC. Prove: has all right angles. [CBSE 2012, Given: In ∆ABC and ∆DEF, AB = DE, AB || DE, BC = EF and BC || EF. Given: In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ.To Prove: (i) ∆APD ≅ ∆CQB(ii)     AP = CQ(iii)    ∆AQB ≅ ∆CPD(iv)    AQ = CP(v)     APCQ is a parallelogram.Construction: Join AC to intersect BD at O.Proof: (i) In ∆APD and ∆CQB,∵ AD || BC| Opposite sides of parallelogram ABCD and a transversal BD intersects them∴ ∠ADB = ∠CBD| Alternate interior angles⇒ ∠ADP = ∠CBQ    ...(1)DP = BQ    | Given (2)AD = CB    ...(3)| Opposite sides of ||gm ABCD In view of (1), (2) and (3)∆APD ≅ ∆CQB| SAS congruence criterion(ii)    ∵ ∆APD ≅ ∆CQB| Proved in (i) above∴ AP = CQ    | C.P.C.T. Given: Quadrilateral ABCD is a parallelogram Prove: Triangle DAC is congruent to triangle BCA 2. Solution: sides of || gm ABCD∴ ∆AQB ≅ ∆CPD | SAS Congruence Rule(iv) ∵    ∆AQB = ∆CPD| Proved in (iii) above∴ AQ = CP    | C.P.C.T. In a triangle ABC, P is a point on side BC such that BP:PC=1:2 and Q is a point on AP such that PQ:QA=2:3. Lines form rt . BD BD 7. Title: Given: Parallelogram ABCD with diagonal Author: Glenn Clemens Last modified by: GLENN Created Date: 6/6/2013 8:57:00 PM Company: Home Other titles The main topics covered in NCERT Solutions for Class 9 Maths Chapter 8 are given below: 8.1 Introduction of quadrilaterals 8.2 Angle Sum Property of a Quadrilateral 8.3 Types of Quadrilaterals 8.4 Properties of a Parallelogram 8.5 Another Condition for a Quadrilateral to be a Parallelogram 8.6 The Mid-point Theorem 8.7 Summary ABCD Statement Justification 1. geometry trigonometry euclidean-geometry quadrilateral (v)    ∵ The diagonals of a parallelogram bisect each other.∴ OB = OD∴ OB - BQ = OD - DP| ∵ BQ = DP (given)∴ OQ = OP    ...(1)Also, OA = OC    ...(2)| ∵ Diagonals of a || gm bisect each otherIn view of (1) and (2), APCQ is a parallelogram. ABCD is a parallelogram. Quadrilateral ABCD is a parallelogram. To Prove: (i) ABCD is a square. In parallelogram ABCD, ∠A = 3 times ∠B. prove that BC=CD - 1753581 3 4 6. © Given : A is the centre of the circle. In Fig. If ∠Bac = 35°, Then ∠Abc = - Mathematics. KSEEB Solutions for Class 9 Maths Chapter 7 Quadrilaterals Ex 7.1 are part of KSEEB Solutions for Class 9 Maths. If the diagonals of a parallelogram are equal, then show that it is a rectangle. Prove: AABC AADC fullscreen. Show that:(i)     quadrilateral ABED is a parallelogram(ii)    quadrilateral BEFC is a parallelogram(iii)   AD || CF and AD = CF(iv)   quadrilateral ACFD is a parallelogram, (v)     AC = DF(vi)    ∆ABC ≅ ∆DEF. 10.43 two circles intersects at any two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P,Q respectively.Prove that ∠ACP = ∠QCD. Sie können Ihre Einstellungen jederzeit ändern. The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Given: Diagonal AC of a parallelogram ABCD bisects ∠A.To Prove: (i) it bisects ∠C also. (ii) In ∆BDA and ∆DBC,BD = DB    | CommonDA= BC| Sides of a square ABCDAB = DC| Sides of a square ABCD∴ ∆BDA ≅ ∆DBC| SSS Congruence Rule∴ ∠ABD = ∠CDB    | C.P.C.T.But ∠CDB = ∠CBD| ∵ CB = CD (Sides of a square ABCD)∴ ∠ABD = ∠CBD∴ BD bisects ∠B.Now, ∠ABD = ∠CBD∠ABD = ∠ADB | ∵ AB = AD∠CBD = ∠CDB | ∵ CB = CD∴ ∠ADB = ∠CDB∴ BD bisects ∠D. ac bisects bad. Advertisement Remove all ads. BE — ≅ BE — by the Refl exive Property of Congruence. Now, in quadrilateral OERF OE || FR and OF || ER So, OERF is a parallelogram. "Question 6 Diagonal AC of a parallelogram ABCD bisects ∠A (see the given figure). Given 5. Defn Midpoint 4. Yahoo ist Teil von Verizon Media. therefore, using the above rule we get