Show that:(i) ABCD is a square(ii) diagonal BD bisects ∠B as well as ∠D. ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C.Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D. Show that i) it bisects ∠C also, ii) ABCD is a rhombus. Diagonal AC of a parallelogram ABCD bisects ∠A (see the given figure).Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.If in parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ, then ΔAPD ≅ ΔCQB by SAS congruence, AP = CQ, ΔAQB ≅ ΔCPD by SAS congruence, AQ = CP, and APCQ is a parallelogram. NCERT Maths Solutions Class 9 Chapter 8 Exercise 8.1 Question 9 Show that: (i) ΔAPD ≅ ΔCQB (ii) AP = CQ (iii) ΔAQB ≅ ΔCPD (iv) AQ = CP (v) APCQ is a parallelogram Video Solution: In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see Fig. ☛ Check: NCERT Solutions Class 9 Maths Chapter 8 Since opposite sides in quadrilateral APCQ are equal to each other, thus APCQ is a parallelogram. ![]() (v) From the result obtained in (ii) and (iv), AQ = CP and AP = CQ ∴ ΔAQB ≅ ΔCPD (Using SAS congruence rule) ∠ABQ = ∠CDP ( Alternate interior angles for AB || CD) Click on the button below to turn the pure parallel lines into a parallelogram. In parallelogram Opposite sides are equal Opposite angles are equal Diagonals bisect each other Sum of adjacent angles is 180° In parallelogram, Opposite angles are equal DCB BAD Ex 3.3, 1 Given a parallelogram ABCD. ∴ ΔAPD ≅ ΔCQB (Using SAS congruence rule)ĪB = CD (Opposite sides of parallelogram ABCD) To create a parallelogram just think of 2 different pairs of parallel lines intersecting. ![]() ∠ADP = ∠CBQ (Alternate interior angles for BC || AD)ĪD = CB (Opposite sides of parallelogram ABCD) Given: ABCD is a parallelogram and DP = BQ ![]() In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see Fig.
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